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AN INTRODUCTORY LOGIC 



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THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO 
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MACMILLAN & CO., Limited 

LONDON • BOMBAY • CALCUTTA 

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THE MACMILLAN CO OF CANADA, Ltd. 

TORONTO 



AN 



INTRODUCTORY LOGIC 



BY 



JAMES EDWIN CREIGHTON 

SAGE PROFESSOR OF LOGIC AND METAPHYSICS IN CORNELL 
UNIVERSITY 



THIRD EDITION, REVISED AND ENLARGED WITH THE ADDITION 
OF NEW PROBLEMS AND EXAMPLES 



THE MACMILLAN COMPANY 

LONDON : MACMILLAN & CO., Ltd. at 

1909 ^^ 5 

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All rights reserved .y and, 



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Copyright, 1898, 1900, 1909, 
By the MACMILLAN COMPANY. 



Set up and electrotyped September, 1898. Reprinted July, 1899. 

Second Edition, Revised and Corrected, March, 1900. 

Third Edition, Revised and Enlarged. Published September, 1909. 



CI. A 2'4'649 9 

SEP 'Yi'md 



J. S. Gushing Co. — Berwick & Smith Co. 
Norwood, Mass., U.S.A. 



PREFACE 

This volume is intended primarily as a text-book for 
college students, and grew out of my lectures on Logic 
to undergraduate classes in Cornell University. It aims 
at being both practical and theoretical. In spite of 
the obvious deficiencies of formal Logic as a theory of 
the nature of thought, I am convinced that it is one 
of the most valuable instruments in modern education 
for promoting clear thinking, and for developing criti- 
cal habits of mind. J. S. Mill, speaking in the Auto- 
biography of the discipline which he received from work- 
ing logical exercises, expresses the following opinion : 
*' I am persuaded that nothing, in modern education, tends 
so much, when properly used, to form exact thinkers, who 
attach a precise meaning to words and propositions, and 
are .not imposed on by vague, loose, or ambiguous terms." 
Although in treating the syllogistic Logic I have followed 
to a large extent the ordinary mode of presentation, I have 
both here, and when dealing with the Inductive Methods, 
endeavoured to interpret the traditional doctrines in a 
philosophical way, and to prepare for the theoretical dis- 
cussions of the third part of the book. 

The advisability of attempting to include a theory of 
thought, or philosophy of knowledge, even in outline, in 
an elementary course in Logic, may at first sight appear 
doubtful. It seems to me, however, that this inclusion 
is not only justifiable, but even necessary at the present 
time. Psychology is no longer a ^ philosophy of mind ' ; 
but, under the influence of experimental methods, has 
differentiated itself almost entirely from philosophy, and 



vi Preface 

become a * natural ' science. As a natural science, it is 
interested in the structure of the mental life, — the char- 
acteristics of the elementary processes, and the laws of 
their combination, — and not primarily in the function 
which ideas play in giving us knowledge. It is clear that 
psychology does not undertake to give a final account of 
all that mind is and does. It belongs to Logic to investi- 
gate inteUigence as a knowing function, just as it is the 
task of Ethics to deal with the practical or active mental 
functions. 

The practical question still remains as to whether this 
side of Logic can be made profitable to students who have 
had no previous philosophical training. I am well aware 
of the difficulty of the subject, but my own experience 
leads me to believe that the main conceptions of modern 
logical theory can be rendered intelligible even to ele- 
mentary classes. Of the incompleteness and shortcomings 
of my treatment I am quite conscious ; but I have en- 
deavoured to make the matter as simple and concrete as 
possible, and to illustrate it by means of familiar facts 
of experience. 

For a number of the practical questions and exercises, 
I am indebted to Professor Margaret Washburn of Wells 
College ; others are original, or have been collected in the 
course of my reading. I have also taken a number of 
arguments from the examination papers of different uni- 
versities, and from various works on Logic, especially 
from Jevons's Studies in Ded^ictive Logic^ from the little 
volume entitled Qttestions on Logic by Holman and Irvine 
(2d ed., London, 1897), and from Hibben's Inductive Logic. 

In writing the book, I have been under obligation to 
a large number of "writers and books. My heaviest debt 
is doubtless to Bosanquet, and perhaps next in order I am 
under obligations to Mill, Jevons, Sigwart, and Bradley. 
I have also derived help from Minto's Logic, Deductive 



P7^eface vii 

and Inductive, the chapter on ' Reasoning ' in James's 
Principles of Psychology, J. H. Yiy&Xo'^'' ^ Ele7nents of Logic, 
and from other works to which reference is made through- 
out the book. 

My colleagues in the Sage School of Philosophy have 
kindly aided me from time to time with advice and encour- 
agement, and I have also received valuable suggestions 
from other teachers of Logic with whom I have talked 
and corresponded. In particular, I wish to express my 
obHgations to my former colleague, Professor James Seth, 
who read nearly all of the book in manuscript, and to 
Dr. Albert Lefevre, who kindly assisted me in reading 

the proofs. 

J. E. C. 

Cornell University, 
August, 1898. 



PREFACE TO THIRD EDITION 

The present edition represents a somewhat thorough 
revision of this book, which had remained substantially 
unchanged since its first publication, eleven years ago. 
Changes of more or less importance have been introduced 
into every chapter ; new paragraphs have been added to 
many of the sections ; and, especially in the Second Part, 
many of the sections have been entirely rewritten. Chap- 
ter XIII. of the old text, on the "Problem of Induction," 
has been expanded into two chapters ; and, throughout 
this Part, an attempt has been made to bring the treatment 
of the various inductive methods into closer relation with 
a general philosophical theory. The chapter with which 
the text formerly closed, '* Rational and Empirical Theories," 
has been replaced by one entitled ** The Unification of 
Knowledge." It has seemed important to conclude the 
discussion of the nature of thought with some statement 
of the meaning and function of the main categories which 
experience involves, and, in this connection, to indicate in 
a general way the necessity of a philosophical interpreta- 
tion of the results of the special sciences. The number 
of problems and examples of reasoning to be analyzed has 
been more than doubled in the belief that fresh material 
of this nature will prove welcome to teachers of the subject. 

The two purposes of an introductory course in logic 
which were emphasized in the preface to the first edition — 
to afford discipline in thinking and to furnish an introduc- 
tion to philosophical studies — have thus been kept in mind 

viii 



Preface ix 

in the present revision. The Third Part of the book pre- 
sents an elementary account of knowledge from the devel- 
opmental standpoint. The conceptions there treated in 
a somewhat systematic way are, however, introduced from 
time to time in the earlier chapters to modify and interpret 
the results of the older logical theories. It will be found 
that the more theoretical considerations have generally 
been printed as separate paragraphs in smaller type, and 
may therefore conveniently be omitted, if thought desirable, 
when the time devoted to the subject does not allow a 
consideration of all the topics dealt with in the book. 
These paragraphs are usually intended merely to suggest 
further problems to the student, or to furnish a text to the 
teacher for explanation and elaboration. 

I am indebted to many of my colleagues who have used 
the book in the classroom for helpful criticisms and sug- 
gestions regarding its revision. In particular, I wish to 
acknowledge my obligations to Dr. Edmund H. Hollands 
for many suggestions and much valuable assistance, espe- 
cially in the collection and arrangement of the exam_ples. 
My thanks are also due to Dr. Hollands and to Mr. C. H. 
Williams for aid in proof-reading. 

J. E. C. 

Cornell University, 
August, 1909. 



TABLE OF CONTENTS 



Introduction 

CHAPTER I 
The Standpoint and Problem of Logic 

PAGE 

§ I. Definition of the Subject i 

§ 2. Relation to Psychology 5 

§ 3. Logic as a Science and an Art 9 

§ 4. The Material of Logic 14 

CHAPTER II 

Important Stages in the Development of Logic 

§ 5. Socrates and the Concept . . . . . . . • 19 

§ 6. Aristotle and the Syllogism . . 23 

§ 7. Bacon and the Inductive Method 28 

§ 8. Logic from the Evolutionary Standpoint . . . . .32 

Part I. — The Syllogism 

CHAPTER III 

The Syllogism and its Parts 

§ 9. The Nature of the Syllogism 36 

§ 10. The Parts of the Syllogism 39 

§11. Perception, Conception, and Judgment 44 

CHAPTER IV 

The Various Kinds of Terms 

§ 12. Singular, General, and Collective Terms 49 

§ 13. Abstract and Concrete Terms 51 

§ 14. Positive and Negative Terms .55 

§15. Absolute and Relative Terms 57 

§ 16. Extension and Intension of Terms 58 

xi 



xii Table of Contents 



CHAPTER V 

Definition and Division 

PAGE 

§ 1 7. Fixing the Meaning of Terms 64 

§ 18. Definition 66 

§ 19. Division . . • 77 

CHAPTER VI 

Propositions 

§ 20. The Nature of a Proposition 84 

§21. The Quality and Quantity of Propositions 86 

§ 22. Difficulties in Classification ........ 89 

§ 23. Formal Relation of Subject and Predicate 90 

CHAPTER VII 

The Interpretation of Propositions 

§ 24. The So-called Process of Immediate Inference .... 97 

§ 25. The Opposition of Propositions ....... 99 

§ 26. The Obversion of Propositions . . . . . . . 103 

§ 27. The Conversion of Propositions . . . . . . . 105 

§ 28. Contraposition and Inversion ....... 108 

CHAPTER VIII 

The Syllogism 

§29. The Nature of Syllogistic Reasoning 112 

§30. The Rules of the Syllogism . . . . . . . .115 

§31. The Figures of the Syllogism 120 

CHAPTER IX 

The Valid Moods and the Reduction of Figures 

§32. The Moods of the Syllogism .122 

§ 33. The Special Canons of the Four Figures 123 

§34. The Determination of the Valid Moods in Each of the Figures . 127 
§ 35. The Mnemonic Lines ......... 129 

CHAPTER X 

Abbreviated and Irregular Forms of Argument 

§ 36. Enthymemes 133 

§ 37. Prosy llogisms and Episyllogisms . • • • • •■ • ^34 



Table of Contents ^ s/ xiii 

§38. Sorites, or Chains of Reasoning . . . vV*^ • • • 136 
§ 39. Irregular Arguments >* . . .139 

CHAPTER XI -1 ^^ ^ 

Hypothetical and Disjunctive Arguments 

§40. The Hypothetical Syllogism . . 144 

§ 41. Relation of Categorical and Hypothetical Arguments •. . . 148 

§42. Disjunctive Arguments . 154 

§ 43. The Dilemma . 156 

CHAPTER XII 

Fallacies of Deductive Reasoning 

§ 44. Classification of Fallacies 164 

§ 45. Errors in Interpretation . . . . . . . .166 

§ 46. Formal Fallacies . .170 

§ 47. Material Fallacies . 171 



Part H. — Inductive Methods 

CHAPTER XIII 

The Problem of Induction 

§ 48. The Problem of Induction 190 

§49. The Enumeration of Instances . , . , . . .192 
§ 50. Induction through Analysis 196 

CHAPTER XIV 

The Assumptions of Induction — Stages in the Inductive Procedure 

§51. The Assumptions of Induction 202 

§ 52. Stages in the Inductive Process 205 

§ 53* Observation and Explanation 207 

CHAPTER XV 

Enumeration and Statistics 

§ 54. Enumeration or Simple Counting 216 

§ 55. Statistics and Statistical Methods 220 

§ 56. The Calculation of Chances 228 



xiv Table of Contents 



CHAPTER XVI 

Determination of Causal Relations 

PAGE 

§57. Causal Connection 234 

§ 58. Mill's Experimental Methods . . . . . . .237 

§ 59. The Method of Agreement 239 

§ 60. The Method of Difference 244 



CHAPTER XVH 

Determination of Causal Relations {continued') 

§61. The Joint Method of Agreement and Difference .... 249 

§ 62. The Method of Concomitant Variations 255 

§ 63. The Method of Residues 260 

CHAPTER XVIII 

Analogy 

§ 64. Explanation by Analogy 266 

§ 65. Analogy as Suggestive of Explanatory Hypotheses . . .271 
§ 66. The Incompleteness of Analogical Reasoning .... 274 



CHAPTER XIX 

The Use of Hypotheses 

§ 67. Reasoning from an Hypothesis 278 

§ 68. Formation of Hypotheses 282 

§ 69. The Proof of an Hypothesis 285 

§ 70. Requirements of a Good Hypothesis 293 



CHAPTER XX 

Fallacies of Induction 



§ 71. The Source of Fallacy 

§ 72. Fallacies due to the Careless Use of Language 

§ 73. Errors of Observation ..... 

§ 74. Mistakes in Reasoning ..... 

§ 75. Fallacies due to Individual Prepossessions . 



298 
299 
303 
309 
312 



Table of Contents xv 

Part III. — The Nature of Thought 

CHAPTER XXI 

Judgment as the Elementary Process of Thought 

PAGE 

§ 76. Thinking the Process by which Knowledge grows or develops . 316 

§ 77. The Law of Evolution and its Application to Logic . . .317 

§ 78. Judgment as the Starting-point 322 

§ 79. Concepts and Judgment 324 

CHAPTER XXII 

The Main Characteristics of Judgment -.. 

§ 80. The Universality of Judgments 329 

§81. The Necessity of Judgments . . . . . . . •331 

§ 82. Judgment involves both Analysis and Synthesis .... 334 

§ 83. Judgment as constructing a System of Knowledge . . . 339 

CHAPTER XXIII 

The Laws of Thought 

§ 84. The Law of Identity 343 

§ 85. The Law of Contradiction . 350 

§ 86. The Law of Excluded Middle . 352 

CHAPTER XXIV 

Types of Judgment 

§ 87. Judgments of Quality 3^5 

§ 88. Judgments of Quantity 3^8 

§ 89. Judgments of Causal Connection 362 

§90. Judgments of Individuality 370 

CHAPTER XXV 

The Nature of Inference. — Induction and Deduction 

§ 91. Judgment and Inference . . . . . , . . 373 

§ 92. The Nature of Inference ........ 378 

§ 93. Induction and Deduction 384 



XVI 



Table of Contents 



CHAPTER XXVI 

The Unification of Knowledge 



§ 94. Science and Philosophy .... 

§ 95. Science as Philosophy ..... 

§ 96. The Assumptions of the Sciences . 

§ 97. Philosophy as the Interpretation of the Sciences 



Questions and Exercises 

Miscellaneous Exercises in Propositions 
Miscellaneous Examples of Deductive Arguments 
Miscellaneous Examples of Inductive Arguments 



PAGE 

390 
395 

399 
405 

409 

424 

435 
469 



Index . 517 






INTRODUCTION 

CHAPTER I 

THE STANDPOINT AND PROBLEM OF LOGIC 

§ I. Definition of the Subject. — Logic may be defined as 
the science of thought, or as the science which investigates 
the process of thinking. Every one knows, in a general way 
at least, what is meant by thinking, and has noticed more or 
less consciously some of its peculiarities. Thinking is the 
intellectual act by means of which knowledge is obtained. 
We do not really know any fact until we think it; that is, 
until the mind sets it in its proper relation to the other parts of 
its experience, and thus comes to understand its true mean- 
ing. We make a distinction, for example, between what has 
come to us through report or hearsay, and conclusions which 
we have reached by our own thinking. ' I have heard j^ we 
say, ^ that A is dishonest, but I do not know iV That is, 
this fact has not been reached as a result of our own thinking, 
and cannot therefore claim the title of knowledge. On the ^ 
other hand, that the earth is round, is not a mere matter of 
hearsay for an educated man. It is a piece of knowledge, 
because it is a conclusion which he has reached by thinking, 
or by putting together various facts for himself. 

Logic, then, is the science which treats of the operations of 
the human mind in its search for truth. Logic must always 



2 The Standpoint and Problem of Logic 

assume that the thinking which it investigates has, as its 
aim and object, the attainment of truth. Thinking is thus 
an expression of the will as well as of the intelligence. Again, 
as seeking truth, thinking is not a mere arrangement of ideas 
in our heads, but is a dealing with the nature of objects. 
Thought cannot exist in itself or by itself as something merely 
in our minds, but it is its very nature to refer to real things, 
existing in an objective world. This follows directly from 
our definition of thought as concerned with truth. Truth 
is no private state of the subjective mind, but something 
objective that is, in a sense, independent of the individual 
thinker and his ideas. 

In defining Logic as a science, we mean that it seeks to 
substitute exact and systematic knowledge regarding the 
nature of thought for the popular notions to be found in 
everyday life. Like all the sciences, logic has to correct 
and supplement ordinary knowledge. It is its mission to 
help us to understand more exactly and completely the way 
in which thinking goes on, and to enumerate and describe, as 
fully and precisely as possible, the various modes and types 
of thought which are employed in gaining knowledge. 

But it is also the business of a science to systematize facts. 
Logic, then, cannot content itself with a mere description of 
this or that kind of thinking, in isolation from other ways 
in which we think. It must also deal with the way in which 
the various kinds of thinking are related. For example, we 
apply such terms as ^ conception,' ^judgment,' ^ induction,' 
and ^deduction' to different intellectual operations, and give 
the distinguishing characteristic in each case. But it is neces- 
sary as well to understand how these processes are related. 
Since all thinkjng has one end, the discovery of truth, the 



§ I. Definition of the Subject 3 

various intellectual operations must mutually cooperate and 
assist in this result. All of the logical processes, then, stand 
in relation to one another. They are all parts of the one in- 
telligence, though they may well represent different stages or 
steps in its work of obtaining knowledge. It is therefore 
the business of logic to show us the organic structure of 
thought. In other words, Logic must furnish a compre- 
hensive view of the way in which intelligence acts, and the 
part which processes like ^ conception,' ' judgment,' ^ induc- 
tion/ etc., play. 

(i) The word ^ logic ' is derived from the adjective corresponding 
to the Greek noun Aoyo?, which signifies either a complete thought, 
or a word as the expression of that thought. The singular form of 
the adjective XoyiKrj^ from which the English word is derived, was 
supposed to qualify either €7rto-T>7/x77, as applying to the theoretical 
science of logic, or rixvrj, as referring to the practical application 
of its rules and as affording guidance in the art of correct reason- 
ing. We shall have to raise the question in a subsequent section 
how far it is possible to regard logic as an art, or a system of rules 
which teach us how to reason correctly. 

The use of the same term (Xdyo?) by the Greeks to denote 
both^ thought,' and ^ word' or ^ discourse,' emphasizes the close and 
vital relation between thought and its expression in language. 
Whether thinking can go on without language is a psychological 
question that we cannot here decide. But it is certain that in 
adult human thinking the thought and its verbal expression are 
inseparably connected, just as the principle of life is connected with 
the functions and activities of the physical organism. The word 
is no arbitrary or external mark attached to a ready-made thought 
which exists independently. The verbal expression is rather the 
means in which and through which the thought completes itself. 
It is that which gives to the thought, not only a name, but an abid- 



4 The Standpoint and Problem of Logic 

ing reality as a permanent possession. To introduce a new term 
into a science is not indeed always a great intellectual achievement. 
New names may be coined for facts and conceptions that are 
already familiar. But, on the other hand, new thoughts and dis- 
coVeries must find expression either in the employment of new 
terms, or in the use of old terms in a new and more definite sense. 

What has been said will suffice to make clear the close relation 
between Logic and Rhetoric. Logic finds the products of think- 
ing expressed in language, and to a considerable extent may be said 
to be concerned with the meaning of words, sentences, and spoken 
or written arguments. It is impossible to make any sharp divi- 
sion between the thoughts and their relations, on the one hand, and 
the form of the words and sentences with which rhetoric concerns 
itself, on the other. We may say, then, that definiteness of thought 
is a condition of clearness and accuracy in the use of language, and 
also that the effort to express oneself with clearness and pre- 
cision demands and involves logical pains and exactness. Indeed, 
clear thinking and accurate verbal expression are one and in- 
separable, as are also careless or indolent ways of thinking and slip- 
shod and slovenly use of language. By taking the trouble to ex- 
press oneself with precision one forms the habit of thinking rightly. 

(2) We have defined logic as the science of the operations and 
processes of thought, or as the science of thinking. It is evident, 
however, that this definition does not carry us very far unless we 
know what thinking means. And to gain a clearer idea of this com- 
mon term may be said to be the problem of logic. This is, however, 
by no means as easy a task as may at first appear. Familiar words 
and phrases often conceal difficulties. They are constantly repeated 
without reflection, and this very frequency of repetition is likely 
to prevent us from trying to gain any clear ideas regarding the 
nature of the objects which they denote. It is only when we 
become discontented with our knowledge regarding any subject, 
when doubts arise whether we really understand the meaning of 



§ 2. Relation to Psychology 5 

the words which we use, that we attempt to make our knowledge 
scientific, i.e.^ to gain clear, definite, and systematic ideas. This 
can perhaps be made clearer by considering the main differences 
between an educated and an uneducated man. The educated man 
has, of course, a great deal more information than the other, and 
his knowledge is more definite and systematic. But a second and 
more important distinction is found in the attitudsof mind which 
education begets. The educated man is desirous of knowing more, 
because he is sensible of his own ignorance. The uneducated 
man, on the other hand, supposes that he knows all about things 
whose names are familiar to him. He can settle puzzfing theo- 
logical or political problems off-hand in a way which is perfectly 
satisfactory to himself, without study, and almost without reflec- 
tion. 

§ 2. Relation to Psychology. — It may aid us in obtain- 
ing a clearer view of what thinking is, if we compare the 
general standpoint of logic with that of psychology. Both 
of these sciences deal wath what goes on in mind or con- 
sciousness, and are thus opposed to the so-called objective 
sciences, which are all concerned with some group or field 
of external facts. But, in spite of this agreement, there 
is an important distinction between logic and psychology. 
In the first place, psychology deals with all that there is 
in mind. It describes pleasures and pains, acts of will, 
and the association of ideas, as well as what is usually called 
logical thinking. But logic does not differ from psychol- 
ogy simply by being less inclusive than the latter. I^ is 
true that, from the standpoint of psychology, the thought- 
process is merely a part of the mental content, which has 
to be analyzed and described like anything else which 
goes on in consciousness. Thinking has doubtless for 



6 The Standpoint and Problem of Logic 

psychology peculiar marks or characteristics which dis- 
tinguish it from other related processes like those of asso- 
ciation ; but when these have been found, and the psycho- 
logical description of thinking is complete, the question 
with which logic deals has not yet been raised. For logic, 
as we shall see presently, adopts a different standpoint, 
and investigates with a different end in view. 

The important difference is this: In psychology we are 
interested in the content of consciousness for its own sake^ 
and just as it stands. We try to find out what actually 
goes on in our minds, and to describe it just as we should 
any event which occurs in the external world. But in logic 
the question is not: What are mental processes? but rather: 
What knowledge do they give us, and is this knowledge 
true or false? Logic, in other words, does not regard the 
way in which ideas exist, and is not interested in ihtm. for 
what they are, but rather in the purpose which they sub- 
serve in affording us knowledge of something beyond them- 
selves. Psychology, in its description of conscious states, 
inquires regarding their quality, intensity, duration, etc., 
and the ways in which they combine with each other to 
form complex ideas. The problem with which logic is 
concerned, on the other hand, has reference to the value 
of ideas when they are taken to represent facts in the real 
world. As we have already seen, thinking is the pursuit 
of truth ; and, in dealing with thoughts, logic has to describe 
and evaluate them in relation to this end. Hence for logic 
thoughts are true or false, i.e.^ they are in harmony 
or not in harmony with truth, which is the standard or 
norm that thought sets up as its purpose or end. , Psychol- 
ogy, on the other hand, does not ask at all whether the 



§ 2. Relation to Psychology 7 

ideas are true or false, good or bad. It does not seek to 
evaluate ideas in the light of some standard, but confines 
itself to describing their actual mode of existence. 

Consider a little further the nature of the ideas with which 
logic deals. Every idea, as we have seen, not only exists 
in some definite fashion in some particular consciousness, 
connected with certain other ideas, and with a definite 
quality, intensity, etc., but it has a meaning or significance 
as a piece of knowledge. It not only is something, but 
it also stands for or signifies something. Now it is not 
with the existence, but with the meaning side of ideas that 
logic has to do. A logical idea, or piece of knowledge, 
is not merely a modification of consciousness which exists 
in the mind of some individual at a particular time. For 
example, the proposition: ' The three angles of a triangle are 
equal to two right angles,' will give rise to a number of 
definite psychological processes (probably auditory or 
visual in character) in the mind of any individual. These 
processes would also probably differ in character in the 
case of two persons. The meaning of the proposition, 
however, is distinct from the definite processes which arise 
in particular minds. The proposition has a significance 
as an objective fact, or piece of knowledge, outside my 
individual mind; the psychological images or processes may 
differ for different persons, but the fact expressed is the 
same for all minds and at all times. 

(i) The relation between logic and psychology may perhaps be 
illustrated by referring to that which exists between morphology 
and physiology. Morphology deals with the form and structure 
of living organisms, and physiology with the various acts and func- 
tions which these organisms discharge in fulfilling the ends of life. 



8 The Standpoint and Problem of Logic 

Thus we speak of the former as the science of form or structure, 
and of the latter as the science of function. In the same way, 
psychology may be said to deal with the actual structure of mental 
processes, and logic with the part which they play in giving us 
knowledge. 

It must be noticed, however, that this is a distinction made for 
purposes of investigation, and does^ not denote that structure and 
function have nothing to do with each other. On the contrary, 
some knowledge of the function is often necessary in order to under- 
stand the structure of an organ; and, on the other hand, it is usually 
true that the nature of a function only becomes completely intelligi- 
ble when the character of the mechanism with which it works is 
known. And the same holds true, I think, of the relations between 
psychology and logic. Although it has been found profitable when 
dealing with consciousness, as in the biological realm, to investigate 
the nature of structure and function separately, yet here, as there, 
the two lines of inquiry cross each other; for it is beyond question 
that the knowledge we obtain by thinking is largely dependent upon 
the character (quality, intensity, etc.) of the actual processes in con- 
sciousness. To understand the nature of a logical idea, then, it is 
often necessary to refer to the psychological facts and their actual 
mode of behaviour. And it is equally true that one cannot carry 
on a psychological investigation into the nature of mental processes 
without taking account, to some extent, of the part which they play 
in giving us knowledge. No psychology is able to take ideas simply 
as existing conscious processes to which no further meaning or 
importance attaches; it is only with reference to the function they 
perform as knowing states that their own peculiar character can be 
understood. In other words, the intellectual activities and purposes 
of mind must be presupposed in psychology, though this science, for- 
the most part, goes its way as if the ideas were not cognitive at all. 
At least this seems to be true of the ^new' or experimental psy- 
chology, as opposed to the older philosophies of mind. 



§ 3- Logic as a Science a7td an A^^t g 

(2) It would of course be presumptuous, as well as utterly useless, 
for any writer to draw a hard and fast line between logic and psy- 
chology, and to forbid others to overstep it. In attempting to dis- 
cover the dividing line between two closely related sciences, one 
must be guided by the procedure of those who are working in the 
fields which it is proposed to divide. Now, it must be admitted that 
by no means all of the recent writers in psychology limit the sphere 
of their science in the way above described; that is, there are 
certain psychologists who-do not confine their attention to the mere 
mental processes as such, but include in their investigations the fur- 
ther problem regarding the function which these processes play in 
giving us knowledge. Thus in Professor James's Principles oj 
Psychology there is an excellent chapter on ' Reasoning,' which cer- 
tainly contains as much logical as psychological matter. In gen- 
eral, one may say that at the present time psychologists are tending 
to deal with mind more from a ^ functional ' than a ' structural ' point 
of view. That is, the tendency is now to emphasize the activities of 
conscious life, and thus to interpret mind in the light of the 
results it achieves, rather than to explain it solely in terms of the 
elements of which it is composed. But this functional psychology 
is not identical with logic. For, in the first place, it does not limit 
itself, as the latter does, to the cognitive functions of mind. And, 
secondly, it tends to interpret even ideas and judgments in their 
relation to the life of the psychophysical organism in general, 
rather than as elements in the life of reason or truth. It is only 
logic which looks at mental Hf e definitely and exclusively from this 
point of view. For logic, the thinking process is not a mere aspect 
of living, but something to be investigated and understood solely 
in its relation to truth, or the rational consistency which is its 
end and goal. 

§ 3. Logic as a Science and an Art. —We have defined 
logic as the science of thought, but it has often been pointed 



10 The Standpoint and Problem of Logic 

out that there are equally strong reasons for considering 
it to be an art. The purpose of logical study, it is often 
said, is to help us to think correctly, to prevent us from 
falling into errors in our own reasoning, and from being 
misled by the fallacious arguments of others. The difference 
between a science and an art in general is that a science is 
interested in the discovery of facts and laws without any 
thought of what use may be made of this knowledge; an art, 
on the contrary, gives practical guidance and direction for 
some course of action. The question before us, then, is 
this: Does logic merely give us knowledge about the ways 
in which we think, or does it also help us to think rightly? 

Before we attempt to answer this question, we must 
note that practical rules of action are based upon scientific 
knowledge. An art, in other words, depends upon science, 
and grows in perfection with the advance of scientific know^- 
ledge. Thus medicine, as the art of healing, is founded 
upon the sciences of chemistry, physiology, and anatomy, 
and it is because of the great discoveries which have been 
made in these fields within recent years that it has been 
able to advance with such gigantic strides. Again, the 
art of singing, in so far as it is an art which can be taught 
and learned, depends upon a knowledge of the physical 
and physiological laws of the vocal organs. An art, then, 
always presupposes a certain amount of science, or know- 
ledge, and is simply the application of this knowledge to 
some practical purpose. In some cases, the application is 
very obvious and direct; in others, it is much more difficult 
to determine; but, in general, there is always this relation 
between theory and practice, between knowledge and action. 

From what has been already said, it will be evident that 



§ 3- Logic as a Science and an Art ii 

logic must first be a science before it can become an art. 
Its first business must be to investigate the nature of thought, 
and to attempt to discover the different forms which the 
latter assumes in its work of attaining knowledge. So 
that we were right in defining it as primarily a science. 
But the further question remains: How far is it possible 
to apply the laws of logic, after they have been discovered, 
in such a way as to obtain directions for reasoning correctly 
in every case? Can we not apply our knowledge of the 
laws of thought in such a way as to get a complete art of 
reasoning, just as the laws of chemistry and biology are 
appHed in medicine? 

It is no doubt true in logic, as everywhere, that scien- 
tific knowledge is capable of practical application. But 
I do not think that logic can be regarded as an art, in the 
sense that it furnishes a definite set of rules for thinking 
correctly. There is an important distinction in this case 
which must not be left out of account. The physical, 
and even the biological sciences, deal with things whose 
way of acting is perfectly definite and uniform. The char- 
acter of any of the physiological functions, as, e.g,^ digestion, 
may be comparatively complex and difficult to determine, 
but it normally attains its end through the use of the same 
means. When once its laws are understood, it is not dif- 
ficult to prescribe just how the proper means may always 
be secured for the attainment of the desired end. But 
thinking has much more flexibility in its way of acting. 
We cannot say with the same definiteness, as in the cases 
we have been considering, that in order to reach a certain 
end we must use a definite set of means. It is not possible, 
that is, to say: If you would learn what is true about any 



12 The Standpoint and Problem of Logic 

particular subject, you must follow this rule and that in your 
thinking. Logic, it seems to me, cannot be regarded as an 
art like photography, or even like medicine; for it is not 
possible to lay down definite rules for the guidance of think- 
ing in every case. What we can do, is to show the method 
by which new truths have been discovered, and the gen- 
eral conditions which must always be fulfilled in reasoning 
correctly. And it is also possible to point out the more com- 
mon errors which arise when these conditions are violated. 
But it is beyond the power of logic to formulate any definite 
set of rules for the guidance of thinking that can be learned 
and applied as a prescription for every case ; and students 
whose only interest in the subject is the practical one of 
finding some rules that may be directly applied to make 
them infallible reasoners are likely to be disappointed. 

The necessity of devoting oneself to a science quite unself- 
ishly cannot be too strongly enjoined, nor the evils which 
arise when one begins a study ' greedy for quick returns of 
profit,' too often emphasized. Nevertheless, since the question 
has been raised, it would not be just to refuse altogether 
to speak of the practical results arising from a study of 
logic. As we have seen, we cannot hope to become infallible 
reasoners by its aid. It is just as true here as in any other 
field, however, that knowledge is power, and ignorance 
synonymous with weakness. For even if one resolves 
never to look inside a logic book, one must nevertheless 
have some theory, or act upon some principle — it may 
be quite unconsciously — in deciding what is true and 
what is false. For instance, a man may act upon the prin- 
ciple that those things are likely to be true which are favour- 
able to his own interests, or which agree with his own preju- 



§ 3- Logic as a Science and an Art 13 

dices, or with the articles of his church or poHtical party. 
Or again, he may regard his senses as the standards of 
truth. Mr. Bradley says that if dogs reason, they proceed 
upon the principle, ' what smells, exists, and what does 
not smell does not exist.' It is not uncommon to hear 
it announced: What can be perceived through the senses 
is true; what cannot be sensed, or is contrary to the 
testimony of the senses, is an absurdity. This was the 
standard of truth adopted, for example, by those who 
attempted to overthrow the Copernican theory by declar- 
ing it to be in plain contradiction to the testimony of the 
senses. 

It seems evident, therefore, that intellectual beings cannot 
escape some kind of logical theory, whether they hold 
it consciously or unconsciously. It is clear, too, that the 
character of this theory will determine to a great extent 
their thoughts and opinions. The only question which 
remains is whether it is better to leave this matter entirely 
to chance, or to attempt to gain some clear ideas regarding 
the nature of thinking, and the conditions under which 
knowledge arises. It can scarcely be doubted that, even 
from a practical point of view, a true theory is better than 
a false one. A man who has reflected upon the nature of 
proof, and the principles of reasoning, is much less likely 
to be deceived than one who is guided unconsciously by 
assumptions which he has never examined. It is always an 
advantage to know exactly the nature of the result at which 
we are aiming, and to be perfectly clear as to our own pur- 
poses. And this is just what a study of logic aids us in 
attaining. 'It helps us to understand the structure of know- 
ledge and the conditions of proof. Moreover, it engenders 



14 The Standpoint and Problem of Logic 

the habit of criticising propositions, and examining the 
evidence upon which they rest. Further, the importance 
of this study for a theory of education may well be em- 
phasized. For education, at least in so far as it undertakes 
to train the knowing powers of the individual, must be 
based upon a knowledge of the necessary laws of intelligence, 
and of the steps or stages which it passes through in its 
process of development. 

§ 4. The Material of Logic. — The business of logic, 
as we have seen, is to discover the laws of thought and to 
show the differences which exist between real and imaginary 
knowledge. Where now shall we find the materials for 
this study? Where are the facts which are to be taken 
as a starting-point? It is, of course, impossible to learn 
directly from one's own consciousness all that thinking 
is, or everything of which it is capable. For, quite apart 
from the difficulty of observing the process of thought 
while it is actually going on, no one can suppose that his 
own mind furnishes an example of all that thinking has 
done, or can do. It is necessary to take a broader view, 
and learn how other men think. Of course, we cannot 
look into the consciousness of other men, but we can study 
the products and results of their thoughts. The history 
of the way in which truth has been discovered is of the 
greatest importance for logic. We have already spoken 
of thinking as having truth as its standard or norm. It 
is for this reason that logic is sometimes called a normative 
science, since like ethics and aesthetics it looks at the expe- 
rience it studies as realizing an end. But where does logic 
.find its norm ? It has no a priori method of deciding what 
is true and what is false, what is knowledge iind what is 



§ 4- The Material of Logic 15 

not. But in the various sciences of nature and of man, 
we have a body of accepted truth that has been verified 
by the experience of a great many individuals. Now, it 
is to this we must look if we would know what knowledge 
is, and it is in the processes through which it has been built 
up that we find the norm of correct thinking. The history 
of the various sciences furnishes a record of the steps by 
means of which thought has built up knowledge. And, 
in this record, we have also a revelation of the nature of 
the thinking process itself, and of the stages through which 
it has passed in the course of its development. 

It is by a reflection, then, upon the nature of proposi- 
tions which are universally regarded as true that the laws 
of logic are obtained. There is always a permanent body 
of knowledge which no one thinks of calling in question. 
Both in everyday knowledge, and in the sciences, there 
are a great number of propositions which are found true 
by everybody who takes the trouble to verify them. And 
it is here that logic finds its material. Taking the facts 
and propositions which are recognized as certain by every 
one, logic examines their structure in order to learn about 
the nature of the intellectual processes by which they have 
been discovered. What principles, it asks, are involved 
in these bodies of knowledge, and what particular acts of 
thought were necessary to discover them ? It is only by 
examining various pieces of knowledge in this way, and 
attempting to trace out the conditions of their discovery, 
that one can learn anything new regarding the laws 
and character of thought. The best way of getting in- 
formation about what thought can do, is to study what it 
has already accomplished. In other words, there is no 



1 6 The Standpoint and Problem of Logic 

way of learning about thinking except by studying what 
it has done. 

Every piece of knowledge, as the product of thinking, is to some 
extent a revelation of the nature of intelHgence. But scientific 
knowledge — by this I mean the results of the philosophical and 
historical sciences as well as of the so-called natural sciences — 
exhibits perhaps most clearly the nature of thought. For the 
history of these sciences enables us to see the process of know- 
ledge, as it were, in the making. In tracing the history of philo- 
sophical and scientific ideas, we are at the same time following 
the laws of the development of thought. It is this fact which 
makes the history of philosophy and of the various sciences so 
instructive. It was with this object in view, to take but a single 
example, that Whewell wrote his famous History of the Inductive 
Sciences, He was interested, that is, not so much in the mere facts 
and names with which he dealt, as in showing the nature of thinking 
and the methods which had been employed in gaining a knowledge 
of the world. This is made very clear in the introduction to another 
work of Whewell from which I quote: ^^We may best hope to 
understand the nature and conditions of real knowledge by studying 
the nature and conditions of the most certain knowledge which we 
possess ; and we are most likely to learn the best methods of discov- 
ering truth by examining how truths, now universally recognized, 
have really been discovered. Now there do exist among us doc- 
trines of solid and acknowledged merit certainly, and truths of which 
the discovery has been received with universal applause. These 
constitute what we commonly term sciences; and of these bodies of 
exact and enduring knowledge we have within our reach so large a 
collection that we may hope to examine them and the history of 
their formation with a good prospect of deriving from the study such 
instruction as we need seek.'' ^ 

^ Whewell, History of Scientific Ideas^ 3d ed., Vol. I,, p. 4. 



§ 4- The Material of Logic 1 7 

We have been insisting that the materials for the study 
of logic are to be found mainly in the records which we 
possess of what thinking has actually accompHshed. Our 
own consciousness, it was said, can supply but a very 
small quantity of material. To learn what thinking is, 
one must have as broad a survey as possible of its achieve- 
ments. 

But there is another side to the matter. It must never 
be forgotten thatfet is the actual operations of thought with 
which logic is concerned. ) The words and propositions 
which express the results of thinking must never be allowed 
to take the place of the thoughts themselves. Now, we 
cannot directly study the thoughts of any other individual. 
It is only in so far as we interpret, through our own con- 
sciousness, the records of what thinking has done, that 
these records are able to throw any light upon the problem 
of logic. So in this study, as elsewhere, we must find the 
key to the material in our own consciousness. If we are 
to gain any real ideas of the character of the thinking pro- 
cesses by means of which the sciences have been built up, 
we must reproduce these in our own minds. One's own 
consciousness must, after all, furnish the key which makes 
intelligible the account of the various steps which the thought 
of mankind has taken in building up science or knowledge. 
The materials of logic which history furnishes become sig- 
nificant only when translated into acts and operations which 
may be observed in our own minds. 



1 8 The Standpoint and Problem of Logic 

REFERENCES 

The following references may be given in connection with §§ i and 
2: — 
# C. Sigwart, Logic^ Vol. I., General Introduction. 

F. H. Bradley, The Principles of Logic j pp. i-io. 

B. Bosanquet, Logic, Vol. I., Introduction. 

H. L. Mansel, Prolegomena Logica, Chap. I. 

R. Adamson, The first part of the article 'Logic' in the Encyclo- 
pcedia Britannica. 

D. G. Ritchie, The Relation of Logic to Psychology, Philos. Review , 
Vol. v., pp. 585-600; Vol. VI., pp. 1-17. 



CHAPTER II 

IMPORTANT STAGES IN THE DEVELOPMENT OF LOGIC 

§ 5. Socrates and the Concept. — Logic was founded 
as a separate and independent branch of inquiry by Aris- 
totle (387-322 B.C.). Almost from the first beginning 
of philosophical speculation, — which took its rise in the 
sixth century in the Greek cities on the coast of Asia 
Minor, and in Sicily and southern Italy, — questions had, 
however, been raised regarding the nature of knowledge and 
the proper value to be assigned to different forms of expe- 
rience. More paiticularly, these early thinkers emphasized 
the distinction between the knowledge given by sense-per- 
ception and that obtained by thinking or reasoning. The 
latter kind of knowledge, it was generally agreed, is alone 
trustworthy and genuine; while the senses, on the other 
hand, are bad witnesses and do not show us the true nature 
of things. In these early schools, however, logical ques- 
tions about truth and knowledge were largely incidental, 
the fundamental interest being to explain the nature of 
the physical universe. It was not until after the Persian 
wars, when Athens had become the intellectual and com- 
mercial centre of Greece, that the inner world of human 
experience — man's knowledge, moral beliefs, and prac- 
tices, customs, laws, and religions — came to be of primary 
interest and importance to philosophical inquirers. 

19 



20 Important Stages in the Development of Logic 

The political prominence and wealth that came to Athens 
as a result of her leadership in the wars with Persia, led 
to the rapid transformation of the outward appearance of 
the city and also of the life and thought of its inhabitants. 
The new times and the wider circle of political and social 
activities which were thus opened up to citizens of Athens, 
demanded that the older system of education — the tra- 
ditional music and gymnastic — should be supplemented 
by some more advanced instruction. And, in response 
to this demand, there arose a class of teachers called So- 
phists, who made it their business to instruct young men in 
all the practical affairs of life, and especially in the use of 
words and the art of public speaking, or rhetoric, as it was 
called. The Sophists do not seem to have made it their ob- 
ject to teach truth to their pupils, or to inculcate in them a 
love and reverence for truth; they sought rather to make 
those whom they taught clever men of the world. In teach- 
ing the art of argumentation or public speaking they did 
not confine themselves to pointing out the methods by which 
true conclusions could be reached, but went on to teach the 
arts by which the judges could be persuaded, and tricks 
for the discomfiture of one's adversary. The rhetoric of 
the Sophists, in other words, was not a science of reasoning, 
but an art of persuasion and of controversy. It was not 
essential to have any real knowledge of the subject under 
discussion in order to argue well, from their point of view, 
but only to be well versed in all the arts of persuasion, and 
quick to take advantage of an opponent's errors. 

The theory on which the teaching of the Sophists was 
based is usually known as scepticism. The Sophists, that 
is, had come to the conclusion that it is impossible to find 



§ 5- Socrates and the Concept 2i 

any fixed standard of truth. Looking at the diversity 
of individual opinions and of individual feelings, they 
declared that knowledge or truth as something objective, 
or the same for all, is an illusion. Only individual opin- 
ions exist; there is no standard by reference to which these 
opinions may be measured. Indeed, the words ^ truth ' 
and 'falsehood' can have only a practical meaning; each 
individual must be the measure of truth for himself. They 
lacked the scientific spirit that aims at truth which is objec- 
tive and real; like men everywhere whose interest is ex- 
clusively practical, they thought truth in this sense abstract 
and unmeaning, and aimed only at knowledge which has 
some direct application. 

Moreover, in the opinion of the Sophists, the same state 
of things exists with regard to our moral ideas. There 
is no standard of right and wrong, just as there is no stand- 
ard of truth and falsehood. Each man has the right 
to choose what he regards as most advantageous for himself. 
The traditional rules of morality have no authority over 
the individual, nor is it possible to discover any rules of 
morality which are binding on all men. It is the part of 
wisdom to consult one's own interest in acting, and to seek 
to secure one's own advantage. Moral distinctions, like 
logical distinctions, are purely relative and individual. 

Socrates was the great opponent of this doctrine of scep- 
ticism and relativity as taught by the Sophists. They had 
concluded, from the diversity of individual opinion on 
moral questions, that there is no real or absolute distinction 
between right and wrong, false or true. Socrates, however, 
was convinced that if one examined more carefully the 
nature of the judgments which are passed by different 



22 Important Stages in the Development of Logic 

individuals, one would find common elements or ideas. It 
is possible, he believed, to find a definite standard, both in 
matters of theory and in matters of practice. This common 
element, however, is not to be discovered in sensation, or 
in feelings of pleasure and pain ; these experiences are purely 
individual, and can never serve as a universal standard. 
But beneath the diversity of sensation and feelings there 
is the thought, or concept^ which is common to all men. 
When rational beings come to understand one another, they 
must agree as to the nature of the fundamental virtues, — 
justice, temperance, courage, etc. It is true that few men 
have thought about these matters, and are able to express 
their meaning clearly, but every man, as a rational being, 
carries these fundamental notions in his mind. Now, in 
order to refute the moral scepticism of the Sophists (and 
it was this side of their teaching which Socrates especially 
opposed), it is necessary that the ethical notions, or con- 
cepts, which are implicit in the minds of men shall be drawn 
out and carefully defined. How is this to be accomplished? 
Socrates did not undertake to teach men what ideas they 
should hold regarding the nature of any of the virtues; he 
rather made them partners in an investigation, and by 
means of skilful questions tried to assist them in discovering 
the real nature of goodness for themselves. Another point 
to be noticed is that the definition of the various virtues 
was reached as a result of comparing the views of a number 
of individuals. In this way, by comparing the opinions 
of many men of different professions and of different 
grades of society, he was able to separate what was merely 
individual and relative in these opinions from what was 
unchanging and absolute. 



§ 6. Aristotle and the Syllogism 23 

Plato, the disciple of Socrates, continued the work of 
his master. He did not confine his attention wholly to 
the moral conceptions, but showed that the Socratic method 
could also be used to refute the intellectual scepticism of 
the Sophists. In other words, he proved that in the concept, 
or thought, as opposed to sensation, a standard of truth 
is to be found, as well as a standard of morality. Know- 
ledge arises from thinking, and it is possible to compare our 
thoughts, and thus to reach what is objective and real in 
itself, however impossible it may be to find any basis of 
comparison in our sensations. In Plato's Dialogues a great 
many logical questions come up for discussion, and in these 
discussions we can often see some of the fundamental dis- 
tinctions of present day thought and language, as it were, 
in the making. But Plato made no attempt to organize 
and arrange these results into a single science. 

§ 6. Aristotle and the Syllogism. — This work of organi- 
zation was accomplished by Plato's disciple, Aristotle. He 
undertook a thorough investigation of the process of reason- 
ing, and sought to show what conditions and principles are 
necessarily involved in reaching certainty. Aristotle was 
thus the founder of logic, as well as of psychology, zoology, 
and most of the other sciences which have come down to us 
from the ancient world. His most important logical works 
are the Categories^ De Inter pretatione, Prior Analytics, Pos- 
terior Analytics, Topics, and the Sophistical Elenchus, a 
treatise on Fallacies. These writings came afterwards to be 
known as the Organon (or scientific instrument) of Aristotle. 
They contained, in the first place, what we call theory of 
knowledge (a discussion of the structure of knowledge, and 
of the scientific principles upon which it rests), which formed 



24 Important Stages in the Development of Logic 

an essential part of Aristotle's philosophical system. But 
they also furnished the practical application of these prin- 
ciples. In his doctrine of the syllogism, which is found 
mainly in the Friar Analytics^ he showed what are the only 
valid forms of reasoning from general propositions, and thus 
furnished the pattern or type to which all such proofs must 
conform. He also classified, in his work on Fallacies, the 
various species of false reasoning, and showed how false 
arguments could be refuted and exposed by the principles 
which he had discovered. The form to which Aristotle 
maintained that all true reasoning can be reduced was as 

follows: — 

All men are mortal, 

Socrates is a man, 

Therefore Socrates is mortal. 

This is called a Syllogism^ and it is made up of three propo- 
sitions. The first two propositions are called Premises, and 
the last the Conclusion. All reasoning from premises, all 
proof, can be reduced to this form. Of course, the propo- 
sitions which make up the syllogism do not always stand 
in this order, and sometimes one of them may be omitted. 
Thus in the argument: ^ he ought to be supported by the 
state, for he is an old soldier,' the conclusion stands first, 
and one premise is wanting entirely. It is easy to see, how- 
ever, that the real argument when properly arranged is 
equivalent to this: — 

All old soldiers ought to be supported by the state, 

He is an old soldier, 

Therefore he ought to be supported by the state. 

Now the part of Aristotle's logic which was best worked 
out was a theory of proof or demonstration by means 



§ 6. Aristotle and the Syllogism 25 

of the syllogism. Here he showed clearly the various ways 
in which different kinds of propositions could be combined 
as premises to yield valid conclusions, and proved that no 
conclusion could be drawn from other combinations. This 
part of the Aristotelian logic has come down to us almost 
unchanged, and is the subject of Part I. of the present volume. 

It will be noticed that, in the doctrine of the syllogism, 
Aristotle was dealing with that kind of reasoning which 
undertakes to demonstrate the truth of some fact, by show- 
ing its relation to a general principle which every one admits. 
In other words, this part of his work may be called the 
logic of proof or demonstration. Aristotle was at one 
time of his life a teacher of rhetoric, and he seemed always 
to have aimed at putting this art of reasoning on a scien- 
tific basis. That is, for the rules of thumb and questionable 
artifices of the Sophists, he wished to substitute general 
laws and methods of procedure which were based upon 
a study of the principles and operations of reason. By 
complying with the rules which he laid down, an argu- 
ment will necessarily gain the assent of every rational being. 

But we do not employ our reason merely in order to 
demonstrate to ourselves or to others what we already 
know. We seek to discover new facts and truths by its 
aid. In other words, we not only wish to prove what is 
already known, but also to discover new facts, and we 
need a logic of Discovery, as well as a logic of Proof. This 
distinction between proof and discovery corresponds in 
general to that between Deduction and Induction. It is not 
an absolute distinction, as will appear later, for both pro- 
cesses are constantly employed in conjunction. But, for the 
present, it may be said that deduction is the process of show- 



26 Important Stages in the Development of Logic 

ing how particular facts follow from some general principle 
which everybody admits, while Induction shows the methods 
by which general laws are obtained from an observation of 
particular facts. Now Aristotle, as we have seen, furnished 
a very complete theory of Deduction, or method of proof. 
But he did not treat of Induction, or the method of pass- 
ing from particular facts to general laws, with anything 
like the same completeness. Moreover, what he did write 
on this subject received no attention for many centuries. 
Aristotle was himself a great scientific observer, and may 
well be regarded as the father of many of our modern 
sciences. But, in his logical writings, his main object seems 
to have been to present a true theory of argumentation, as 
opposed to the false theories of the Sophists. Science, too, 
was only in its beginning when Aristotle wrote, and it was 
impossible for him to foretell the methods of discovery 
which it has actually employed. 

After Aristotle's death (322 B.C.), and after the loss of 
Athenian independence, there was a great decline of interest 
in matters of mere theory which had no direct application 
to the practical affairs of life. The Stoic school did make 
some slight additions to logical theory, but like their oppo- 
nents, the Epicureans, they regarded practice, the art of 
living well, as the supreme wisdom of life. The Romans, 
who derived their knowledge of Greek philosophy largely 
from the Stoics, were also interested in the practical advan- 
tages of logic, rather than in its theoretical side. It was 
the possibility of applying the laws of logic to rhetoric and 
public speaking which especially interested Cicero, who was 
the first to make Latin paraphrases and adaptations of 
Greek logic in his rhetorical works. 



§ 6. Aristotle and the Syllogism 27 

For more than seven hundred years, during the Middle 
Ages, the Greek language and literature was almost unknown 
in Western Europe. During this time, almost the only 
sources of information regarding logic were Latin trans- 
lations of Aristotle's Categories^ and of an Introduction to 
the same work by Porphyry, who lived 232-303 a.d. Both 
of these translations were made by Boethius (470-525), 
who is best known as the author of The Consolations of 
Philosophy, Even when scholars again -became acquainted 
with the original works of Aristotle, in the latter part of 
the Middle Ages, they did not really understand their true 
significance. They took the husk, one may say, and neg- 
lected the kernel. They adopted the Aristotelian logic 
as an external and arbitrary set of rules for the guidance 
of thinking, and neglected entirely the scientific theory 
upon which these rules were based. A great deal of inge- 
nuity was also shown in subdividing and analyzing all possible 
kinds of argument, and giving the particular rule for each 
case. This process of making distinctions was carried so far 
that scholastic logic became extremely cumbersome and arti- 
ficial. Its pretensions, however, rapidly increased ; it claimed 
to furnish a complete instrument of knowledge, and a sure 
standard for discriminating between truth and falsehood. 

It is not very difficult to understand why this set of logical rules 
seemed so satisfactory to the age of Scholasticism. The men of this 
period had no desire to increase their knowledge; they supposed 
that they were already in possession of everything which was worth 
knowing. Their only object was to weave this knowledge into a 
system, to show the connection and interdependence of all its parts, 
and thus to put it beyond the possibility of attack. And for this 
purpose the school logic was admirably adapted; it was always 



28 Important Stages in the Development of Logic 

possible to bring every case which could arise under one or other of 
its rules. 

There is no doubt that the Aristotelian logic had a real 
value of its own, and that it exercised a very important influence 
upon Western civihzation, even in the form in which it was 
taught by the Schoolmen; but there is, of course, nothing com- 
plete or final about it. Its main purpose, as we have already 
seen, was to furnish a method by means of which the knowledge 
we already possess may be so arranged as to be absolutely con- 
vincing. But the centre of intellectual interest has changed since 
mediaeval times. We are not content merely to exhibit the cer- 
tainty and demonstrative character of the knowledge which we 
already have, but we feel that there is a great deal of importance 
still to be discovered. So that, in modern times, one may say 
the desire to make discoveries, and so add to the general stock 
of knowledge, has taken the place of the mediaeval ideal of 
showing that the traditional doctrines taught by the church are 
absolutely certain and convincing. And when men became con- 
scious of the importance of gaining new knowledge, and espe- 
cially knowledge about nature, they at once saw the necessity for 
a new logic, or doctrine of method, to aid them in the under- 
taking. 

§ 7. Bacon and the Inductive Method. — All the great 
thinkers of the sixteenth and seventeenth centuries saw 
clearly that the school logic is simply a method of showing 
the certainty of the knowledge we already possess, and 
does not aid us at all in making new discoveries. A new 
method, they all declared, was an absolute necessity. The 
new point of view was put most clearly and eloquently 
by the famous Francis Bacon (1561-1626), at one time 
Lord Chancellor of England. Bacon called his work on 
logic the Novum Organum, thus contrasting it with the 



§ 7- Bacon and the Inductive Method 29 

Organon, or logical treatises of Aristotle. An alternative 
title of the work is, True Suggestions for the Interpretation 
of Nature. Bacon begins this work by showing the ad- 
vantages to be gained from a knowledge of nature. It 
is man's true business, he tells us, to be the minister and 
interpreter of nature, for it is only by becoming acquainted 
with the laws of nature that we are ever able to take advan- 
tage of them for our own ends. ''' Knowledge and human 
power are synonymous, since ignorance of the cause pre- 
vents us from taking advantage of the effect." The dis- 
covery of the laws of nature, which is therefore of so 
great practical importance, cannot be left to chance, but 
must be guided by a scientific method. And it is such a 
method which Bacon endeavours to supply in the Novum 
Organum. 

The method which Bacon proposed seems to us very 
simple. If we would gain new knowledge regarding nature, 
he says, and regarding natural laws, we must go to nature 
herself and observe her ways of acting. Facts about nature 
cannot be discovered from logical propositions, or from 
syllogisms; if we would know the law of any class of phe- 
nomena, we must observe the particular facts carefully 
and systematically. It will often be necessary, also, to 
put pointed questions to nature by such experiments as 
will force her to give us the information we want. Know- 
ledge, then, must begin with observation of particular 
facts; and only after we have made a great number of 
particular observations, and have carefully classified and 
arranged them, taking account of all the negative cases, 
are we able to discover in them the general law. No hypoth- 
eses or guesses are to be made ; but we must wait until the 



30 Important Stages in the Development of Logic 

tabulations of the particular phenomena reveal the general 
^form' or principle which belongs to them all. 

It will be frequently necessary to refer to Bacon's work in 
what follows. At present, it is sufficient to note that Bacon 
showed that a knowledge of nature cannot be attained through 
general propositions and logical arguments, but that it is 
necessary to begin with the observation of particular facts. 
He emphasized, also, the importance of systematic obser- 
vation and carefully planned experiments, and showed that 
knowledge must begin with facts of perception. This is 
the method of induction, and Bacon is usually said to have 
been the founder of the inductive sciences of nature. 

Another and quite different method of extending know- 
ledge was proposed by the great Frenchman, Descartes 
(i 596-1650), who took mathematics as the type to which 
all knowledge should conform. That is, he supposed 
that the true method of extending knowledge was to begin 
with general principles, whose truth could not be doubted, 
and to reason from them to the necessary character of 
particular facts. Descartes and his followers thought 
that it was possible to discover certain axiomatic propo- 
sitions from which all truth could be derived through reason. 
They thus emphasized Deduction rather than Induction, 
and reasoning rather than observation and experiment. 
The spirit of Bacon's teaching was, however, continued 
in England by John Locke, in the Essay Concerning Human 
Understanding (1690). During the next centuries, philo- 
sophical thinkers were divided into two great schools : 
Rationalists, or those who agreed in the main with Des- 
cartes ; and Empiricists, or Sensationalists, who followed the 
teachings of Bacon and Locke. 



§ 7- Bacon and the Indttctive Method 31 

Although the natural sciences made great advances 
during the seventeenth and eighteenth centuries, there 
seems to have been no effort made to analyze and describe 
the methods which were actually being employed. In 
England, at least, it seems to have been assumed that all 
discoveries were made by the use of the rules and methods 
of Bacon. One of the first writers to attempt to explain 
the method used by the natural sciences was Sir John Her- 
schel (1792-1871). His work, Discourse on the Study of 
Natural Philosophy ^ was published in 1832. A little later, 
and with the same object in view, William Whewell (1794- 
1866), afterwards Master of Trinity College, Cambridge, 
undertook his History of the Inductive Sciences, which 
was followed some time after by the Philosophy of the Induc- 
tive Sciences, The man, however, who did most towards 
putting the study of logic on a new basis was John Stuart 
Mill (1806-1873), the first edition of whose Logic appeared 
in 1843. We shall have frequent occasion to refer to this 
work in future discussions. It is sufficient to say here 
that Mill continues the empirical tradition of the earlier 
English writers in his general philosophical position. Mill's 
book gave a great impulse to the study of logic. Before 
it was published, writers on the subject had confined their 
attention almost exclusively to the syllogistic or deductive 
reasoning. Mill, however, emphasized strongly the impor- 
tance of induction; indeed, he regarded induction as the 
only means of arriving at new truth, the syllogism being 
merely a means of systematizing and arranging what we 
already know. Though few logicians of the present day 
adopt this extreme view, the importance of inductive methods 
of reasoning, and the necessity of studying them, have 



32 Important Stages in the Develop7nent of Logic 

now become generally recognized. Most modern writers 
on logic devote a considerable amount of attention to induc- 
tion. The reader will find that Part II. of the present volume 
deals with this subject. 

§ 8. Logic from the Evolutionary Standpoint. — There 
is still another side of logic which has been developed 
in the English-speaking world since the time of Mill, though 
it is a direct continuation of the movement started in Ger- 
many by Kant more than a hundred years ago. The so- 
called ^modern' logic has laid aside the formalism and 
paradoxical mode of expression adopted by Hegel, but 
the fundamental conception with which it works — that of 
development — is essentially the same as that employed 
by the latter in his Wissenschaft der Logik (1816-1818). 
It is, of course, true that the work of Darwin in biology and 
the rapid extension of the evolutionary method tended to 
make the older idea of development more concrete and 
render it more attractive. Moreover, evolutionary studies, 
particularly in psychology and anthropology, have contrib- 
uted directly to genetic logic. For logic, from this stand- 
point, seeks to describe and explain intelligence in terms 
of its own development. It looks at the logical mind as a 
system of functions or activities that have a work to do 
and that progressively develop in the capacity to perform 
that work. 

The Aristotelian doctrine of the syllogism is a purely 
formal science. In the form in which it is represented 
in ordinary text-books, it might perhaps be more prop- 
erly described as the art of arranging our knowledge in 
such a way as to compel assent. The ' matter ' with which 
thought is supposed to work is supplied to it in form of 



§ 8. Logic from the Evolutionary Standpoint 33 

concepts and judgments. The problem which formal 
logic has to solve is to define and classify the various kinds 
of concepts with which thought operates, and to determine 
the various relations in which these stand when combined 
into judgments. Similarly, it has to show what combi- 
nations of judgments can be employed as premises leading 
to valid conclusions in the syllogism. The criterion of 
truth employed in these investigations is the principle 
of non-contradiction or consistency. Inconsistent com- 
binations of concepts, that is, are ruled out ; but so far as 
the doctrine of the syllogism goes, anything is true which 
is not self-contradictory. 

Now, without questioning the practical value of its canons, 
it is obvious that formal or syllogistic logic does not take 
any account of many of the processes of everyday thought, 
and that its rules go but a little way in helping us to dis- 
tinguish the true from the false. For, in the first place, 
to think is not merely to combine and arrange ideas already 
in our possession. This might enable us to render clearer 
and more definite what we already know, but would never 
enable us to gain new knowledge. The real movement 
of thought — as opposed to its merely formal procedure 
— consists in the formation of new ideas and new know- 
ledge through actual contact with the world of experience. 
A complete account of the intellectual process, then, must 
deal with the relation of the mind to objects ; it must in- 
vestigate the various activities by means of which thought 
interprets the world and builds up the various sciences 
of nature and of man. 

The recognition of the importance of induction, and 
of the necessity of studying the methods of the inductive 



34 Important Stages in the Developmejtt of Logic 

sciences, which was brought about by Whewell, Mill, and 
others, was a step in the right direction, for it called atten- 
tion to a kind of thinking which occupies a large place in 
our intellectual life, and also gave rise to a truer conception 
of the nature of thought itself. But even Mill did not reach 
the idea which guides modern logicians, namely, that thought 
or intelligence, as the function of interpreting reality, is one 
from beginning to end; and that the various logical opera- 
tions are all parts of one whole, or rather, are ways in which 
intelligence operates in different circumstances, or at differ- 
ent stages of its development. He still tended to treat of 
logical processes, like conception, judgment, and reasoning, 
as if they were separate and distinct processes, each existing, 
as it were, on its own account. In short, we may say that 
Mill was still influenced by an atomistic and static view of 
mind: he does not think of knowledge as essentially all of a 
piece, or of its movement or history as that which reveals its 
nature. 

As opposed to the conception of mind as made up of 
separate ideas, the thought by which modern logic is domi- 
nated is that of the unity and continuity of all intellectual 
life. Thought is regarded as an organic, living function 
or activity, which remains identical with itself throughout 
all its developing forms and phases. The problem, accord- 
ingly, which logic must set before itself is to show the unity 
and interrelation of all of the intellectual processes. No 
one of the steps or stages in this process can be completely 
understood when viewed by itself: each is what it is only in 
and through its connection with the whole of which it forms 
a part. No hard-and-fast boundary lines are to be drawn 
between the different stages of the reasoning process, but 



§ 8. Logic from the Evolutionary Standpoint 35 

it must be shown that the whole nature of intelhgence is 
involved more or less explicitly at each step. So far only 
the broad outlines of this theory have been filled in; but 
the conception of an organism whose parts are developing 
in mutual relation and interdependence promises to be 
as fruitful when applied to logic as it has already shown 
itself to be in the other sciences. 

Besides the ordinary histories of philosophy the reader may con- 
sult for the history of logic: Prantl, Geschichte der Logik im Ahend- 
lande, 4 vols., Leipsic, 1855-1870; which extends, however, only to 
the close of the mediseval period. Harms, Geschichte der Logik, Berlin, 
1 881. Ueberweg, System der Logik, 4th ed., 1874; Eng. trans, of 3d ed., 
London, 1874. Adamson, article 'Logic,' in the Encyl. Brit., 9th ed. Sir 
William Hamilton's Lectures on Logic, also containing much historical 
information. 

Among modern works on logic, the following may be mentioned: 
J. S. Mill, A System of Logic, London, ist ed., 1843; 9th ed., 1875. 
W. S. Jevons, The Principles of Science, London, 1874; 2d ed., 1877. 
Also by the same author. Studies in Deductive Logic, 1880; and Pure 
Logic, 1890. H. Lotze, Logik, 1874; Eng. trans., London, 1881 and 
1888. W. Wundt, Logik, 3d ed., 1 906-1907. C. Sigwart, Logik, 2d ed., 
1889-1893; Eng. trans., London and New York, 1895. 

The newer development of logic is well represented by F. H. Bradley, 
The Principles of Logic, London, 1886. B. Bosanquet, Logic, or the Mor- 
phology of Knowledge, London, 1888; and The Essentials of Logic, Lon- 
don and New York, 1895. L. T. Hobhouse, The Theory of Knowledge, 
London, 1896, may also be mentioned in the same group of writers, 
although he has been, perhaps, more influenced by Mill than by any other 
writer. J. M. Baldwin, Thought and Things, or Genetic Logic, New 
York, 1906-1907, has emphasized especially the genetic processes through 
which logical thinking is built up. 

The following works, among others, have proved useful as text- 
books: W. S. Jevons, Elementary Lessons in Logic, London and New 
York, 1870. A. Bain, Logic, Deductive and Inductive, New York, 
1883. J. N. Keynes, Studies and Exercises in Formal Logic, 4th ed., 
London, 1906. W. Minto, Logic, Inductive and Deductive, New York, 
1894. J. G. Hibben, Logic, Deductive and Inductive, New York, 1905. 



PART I. — THE SYLLOGISM 



CHAPTER III 

THE SYLLOGISM AND ITS PARTS 

§ 9. The Nature of the Syllogism. — The theory of the 
syllogism, as has been already stated (§ 5), was first worked 
out by Aristotle. And it stands to-day in almost the same 
form in which he left it. A few additions have been made 
at different points, but these do not affect materially the 
main doctrine. In dealing with the nature of the syllogism, 
we shall first try to understand its general aim and purpose, 
or the results which it seeks to bring about. We shall then 
have to analyze it into the parts of which it is composed, 
and to examine and classify the nature of these elements. 
Finally, it will be necessary to discover what rules must 
be observed in order to obtain valid conclusions, and to 
point out the conditions which most commonly give rise 
to error or fallacy. 

In the first place, it is to be noticed that syllogistic logic 
deals with the results of thinking, rather than with the 
nature of the thought-process. Its object is not to give 
an account of the way in which thinking goes on, but to 
show how the ideas and thoughts which we already possess 
may be combined, so as to lead to conclusions which are 
certain, and which will compel assent. The ideas which 
the syllogism uses as material are fixed by having been 

36 



§ 9. The Nature of the Syllogism 37 

expressed in language. Indeed, it is largely with words, 
as the expression of thoughts, that syllogistic logic deals. 
Many of the discussions with which it is occupied have 
reference to the proper interpretation of words and propo- 
sitions; and the rules which it furnishes may be taken 
as directions for putting together propositions in such a 
way as to lead to a valid conclusion. Nevertheless, it is 
important to remember that these rules are not arbitrary 
and external, but find their justification in the nature of 
thought. Indeed, the theory of the syllogism, when rightly 
understood, may be said to reveal the fundamental charac- 
teristics of the process of intelligence. For it brings together 
facts in such a way as to make evident their interrelation 
and dependence. It connects a judgment with the grounds 
or reasons which support it, and is thus a process of systema- 
tization. In order to understand the significance of the 
rules of syllogistic logic, then, it will frequently be necessary 
to look beyond words and propositions to the act of thought 
whose results they express. 

A great deal has been written regarding the principles 
or laws of thought, which are employed in all logical reason- 
ing. It seems better, however, to postpone the definite 
consideration of this subject until the student has learned 
more about the various operations of thought, and has had 
some practice in working examples. In dealing with the 
nature and principles of thought, in the third part of this 
book, it will be necessary to discuss this question at length. 
Even at the present stage of our inquiry, however, it is 
important to notice that syllogistic reasoning presupposes 
certain simple and fundamental principles of thought as 
the basis of its valid procedure. In particular, the regular 



38 The Syllogism and its Parts 

syllogism is founded on a principle which we may call 
the law of Identity, or the law of Contradiction, according 
as it is stated affirmatively or negatively. Stated affirma- 
tively, this so-called ^ law ' simply expresses the fact that 
every term and idea which we use in our reasonings must 
remain what it is. A is A, or has the same value and mean- 
ing wherever employed. The law of Contradiction expresses 
the same thing in negative language. A cannot be both B 
and not B. If any term is taken to be the same as another in 
one connection, it must always be taken to be so ; if it is 
different, this relation must everywhere be maintained. The 
data or materials which are employed in the syllogism 
are ideas whose meanings are supposed to be permanently 
fixed and expressed in words which have been carefully 
defined. It would be impossible to reason, or to determine 
the relation of our ideas, if their meaning were to change 
without notice, or if the words by means of which they 
are expressed were used now in one sense and now in another. 
It is true, of course, that our ideas regarding the nature of 
things change from time to time. And, as is evident from 
one's own experience, as well as from the history of language, 
a corresponding change takes place in the meaning of words. 
But the assumption upon which syllogistic reasoning proceeds 
is that the ideas which are to be compared are fixed for 
the meantime, and that the words by which they are ex- 
pressed are used in the same sense throughout the course 
of the argument. The laws of Identity and Contradiction 
are, then, simply the expression, in positive and negative 
form respectively, of the principle of consistency. The one 
fundamental postulate of all thought is that it must be 
consistent with itself. 



§ 10. Tke Parts of a Syllogism 39 

We may, however, have formal consistency without hav- 
ing real truth. It is quite possible that all the require- 
ments of the syllogism may be met without its conclusions 
being true of reality. In other words, an argument may 
h^ formally true, but really false. It is not difficult to 
understand why this may happen. The syllogism accepts 
without criticism the ideas and judgments which it com- 
pares. These data are, of course, the product of previous 
acts of thinking. But in proceeding to arrange them in 
syllogistic form, we do not inquire whether or not they are 
true, i,e, adequate to express the nature of the things for 
which they stand. For the formal purposes of the syllo- 
gism it is only essential that their meanings be clearly under- 
stood, and that these meanings be regarded as fixed and 
permanent. 

§ 10. The Parts of a Syllogism. — The syllogism may 
be said to express a single comprehensive act of thought. 
We may define the reasoning expressed in a syllogism as 
a judgment which has been expanded so as to exhibit the 
reasons by which it is supported. In the syllogism, 

The geranium has five pointed sepals, 
This plant has not five sepals, 
Therefore it is not a geranium, 

we may say that we have the judgment, ^ this plant is not 
a geranium,' supported by the propositions which precede 
it, and that the whole syllogism taken together expresses 
a single thought, which is complete and self-sufhcient. It 
is possible, however, even when one is dealing directly 
with the process of thinking, to distinguish in it different 
subordinate steps, various stages which serve as resting- 



40 The Syllogism and its Parts 

places, in the course of its passage to the complete and 
comprehensive form represented by the syllogism. But 
it is usual, in dealing with the syllogism, to take a more 
external view of its nature, and to regard it primarily as 
made up of words and propositions. 

In this sense, a syllogism can, of course, be divided into 
parts. In the first place, it is composed of three statements, 
or propositions. In the example given above the two 
propositions which stand first are called the Premises, 
since they furnish the grounds or reasons for the propo- 
sition which stands last, and which is known as the Con- 
clusion. However, it is not true that we always find the 
two premises and the conclusion arranged in this regular 
order in syllogistic arguments. Oftentimes the conclusion 
is given first. Frequently, too, one of the premises is not 
expressed, and has to be supplied in order to complete the 
argument. Thus the statement, ^ he must be more than 
sixteen years of age, for he attends the university,' is an 
incomplete syllogism. The conclusion, as will be readily 
seen, stands first. There is also only one premise expressed. 
To put this statement in the regular syllogistic form we 
have to supply the missing premise and arrange it as 
follows : — 

All students of the university are more than sixteen years of age, 

He is a student of the university, 

Therefore he is more than sixteen years of age. 

When one of the premises or the conclusion is not ex- 
pressed, the argument is called an enthymeme. Such an 
argument is defective only in form: the missing premise 
or conclusion is really present and operative in thought. 



§ 10. The Parts of a Syllogism 41 

It is of great importance to form the habit of making clear 
to oneself the premises by which any conclusion claims 
to be supported. In this way groundless assumptions are 
often brought to light, and the weakness of an argument 
exposed. Whenever words like ' therefore/ ^ for/ ' because/ 
^ it follows/ etc., are used in their proper signification, it 
is possible to find an argument composed of two premises 
and a conclusion. But one must not allow oneself to be 
imposed upon by the mere words, but must insist on under- 
standing exactly what are the premises in the case, and 
how the conclusion follows from them. Not only may some 
part of the argument be taken for granted, as a kind of tacit 
agreement, but oftentimes, in arguments as actually used, 
there is a considerable amount of repetition and illustration 
of the principles employed, without any attempt to bring 
these various statements into relation in a formal way as 
premises of a syllogism. To reduce such arguments to 
syllogistic form requires, accordingly, a certain amount of 
interpretation of the statements they contain, involving 
oftentimes both condensation and rearrangement. Such 
reduction of the usual extended form of arguments is usually 
necessary in order to bring out clearly their essential struc- 
ture — the premises which are actually employed to carry 
the conclusion — and to estimate accurately their logical force 
and value. Take, for example, the following passage from 
Jonathan Edwards : — 

Why should we be afraid to let persons who are in an in- 
finitely miserable condition know the truth, or bring them into 
the light for fear it should terrify them ? It is light that must 
convert them if they are ever to be convertedT^^^n^e ease, peace, 



42 The Syllogism a7td its Parts 

darkness and blindness ; therefore as that darkness vanishes and 
light comes in their peace vanishes and they are terrified. But 
that is no good argument why we should endeavor to hold their 
darkness that we may uphold their comfort. 

This may be reduced to the form of two syllogisms 
somewhat as follows : — 

(i) 

The terror of sinners is what dispels their blindness, 

Light is a terror to sinners, 

Therefore light is what dispels their blindness. 

What dispels blindness is really a benefit to sinners, 
Light is what dispels their blindness, 
Therefore light is a real benefit to sinners. 

It is necessary to carry the division of a syllogism still 
farther. Every logical proposition may be divided into 
two Terms, and a Copula or connecting link. The terms, 
which are the extremes of the proposition, are named the 
subject and the predicate. Thus in the proposition, ^ the 
fields are covered with snow,' * the fields ' is the subject, 
' are,' the copula, and ' covered with snow,' the predicate. 
To reduce a proposition to the logical form in which it is 
most conveniently treated, it is necessary to express it in 
such a way that the two terms are united by some part of 
the verb ' to be,' preferably ^ is ' or ^ are.' Thus the sentence^ 
^ No plant can grow without light and heat,' would be 
expressed as a logical proposition in the following, or some 
similar, form : ^ No plant is an organism which can grow 
without light and heat.' ^Men have strong passions ' may 
be written, 'Men are beings having strong passions.' It 
is always well to reduce a sentence to some such form, by 



§ lo. The Parts of a Syllogism 43 

substituting for the verb of predication some part of the 

verb ^ to be.' 

The analysis of the syllogism gives us the divisions under 
which it is convenient to treat this part of logic. We shall 
accordingly deal (i) with Terms, (2) w^ith Propositions, 
and (3) with the Syllogism as a whole. 

These divisions, however, are only made for the sake 
of convenience in treatment. It must not be forgotten 
that a term is a part of a proposition. To understand 
the nature of a term, it is necessary to consider the part 
which it plays in the judgment which the proposition ex- 
presses. In other words, the function of the term, rather 
than the form of the word or words employed, must be 
considered. It is, of course, true that we naturally and 
commonly use certain word forms to express certain kinds 
of ideas, just as in the grammatical sentence the different 
^ parts of speech' — nouns, verbs, etc. — have each a 
definite and comparatively permanent function. But even 
in the sentence it is the part v/hich the word in its grammatical 
function plays, rather than its form, which determines 
whether it is to be classified as a noun or an adjective, a 
preposition or a conjunction. In dealing separately with 
terms, as we propose to do in the next chapter, we shall 
be occupied to a large extent with the/<9rw of words in which 
certain kinds of ideas are usually expressed. But, as the 
same word or group of words may be used for different 
purposes, it will be necessary, in order to understand the 
meaning of terms, to refer frequently to the various ways 
in which they are used in a proposition. 

The same difficulty exists when propositions are con- 
sidered by themselves, the relation to the complete argument 



44 ^^he Syllogism and its Parts 

of which they form a part being thus ignored. In this case, 
however, the results of the isolation are not so apparent; 
for a proposition forms, in a certain sense, a whole by itself. 
It is the expression of a judgment which, as we shall see 
later, is the unitary process of thought. It has thus a sig- 
nificance of its own, as expressing a more or less complete 
and independent act of thought. Nevertheless, it must 
not be forgotten that its independence and completeness are 
only partial and relative. A single proposition cannot 
stand alone. Taken strictly by itself, a proposition is 
only a fragment. In order to make it intelligible, it must 
be brought into relation with the other propositions which 
state the grounds or reasons upon which it rests, or the 
conclusion which it helps to support. The logical nature 
of a proposition will, therefore, depend upon its function 
in an argument, and in treating of propositions this fact 
must not be forgotten. 

§11. Perception, Conception, and Judgment. — Before 
beginning our examination of the elements of the syllogism, 
it is necessary to define some terms that describe certain 
phases or modes of our knowledge. These are Perception, 
Conception, and Judgment. Judgment is both the ele- 
mentary and the universal form of knowing. It includes 
all the others, and uses them as a means to its own end of 
attaining truth. It may, perhaps, be best described as the 
interpreting activity of the mind. At all the stages of 
experience it is at work, construing things in terms of ideas 
or meanings, transforming old ideas in the light of new 
facts, in order to render them more definite and more con- 
sistent. Judgment is thus the form of the general intellec- 
tual activity. To know anything is to express it in terms of 



§ II. Perception^ Conception^ and Judgment 45 

ideas, to qualify it in our thought as this or that, as belonging 
to a certain class of things, or perhaps as differing in some 
respect from another class of things. But it must not be 
supposed that judgment — or any form of thinking — is 
concerned only with our own ideas. Judgment is the 
interpreting, idealizing response of the mind to the real 
world, with which it is always in relation. To think is not 
to play with our own ideas: real thinking deals, more or 
less directly, with a world of real objects and persons. In 
the process of judgment, then, reality is interpreted and 
its meaning expressed in terms of ideas. The expression 
of such an act of thought is a proposition, which, as we have 
already seen, is composed of a subject and a predicate term 
related by means of a copula. 

Now the terms of which a proposition is composed may 
be either Percepts or Concepts, i.e, the result of a perceptive 
act or of a conception. A percept is the result of the mind's 
direct mode of apprehending real things as distinct indi- 
viduals. Hence a percept always refers to ^ this ' or ' that,' 
some distinct individual thing having its own place in space 
or in time. Thus, I perceive, or have a percept of, the 
objects in this room, and of the tree which I see through 
the window. Similarly, one may perceive the particular 
states of consciousness in one's mind. A concept, on the r 
other hand, is a general meaning or idea. It does not refer/ 
directly to some one object of sense. It is not an individual 
embodiment of a particular thing, but is a thought-construc- 
tion, carrying with it the idea of a general nature or mean- 
ing which may apply to a number of individuals. Thus, 
my direct experience of the individual tree at which I am 
looking is a percept, the general idea of tree which I use 



46 The Syllogism and its Parts 

when I say ^ trees are either deciduous or evergreens ' is a 
concept. I may have a percept of the statue of Liberty at 
the entrance to New York harbour ; ^ Hberty/ on the other 
hand, is a concept made up of a more or less definite group 
of meanings, which are unified and held together by the 
word in which it is expressed. 

What, now, is the relation between the percepts and con- 
cepts which are expressed in the terms of a proposition, 
and the judgment which is represented by the proposition 
as a whole ? In the first place, it is to be noted that 
percepts and concepts are the results of previous acts of 
judgment. Ideas are formed only through the mind's own 
act of interpretation ; they never pass over into the mind 
from some external source as ready-made objects. Even 
in the case of perception, where the object seems to be thrust 
upon us, a little reflection will show that the judging 
activity of attention is involved, selecting and arranging 
the various sensation elements, and interpreting them as the 
parts of a single concrete object, in accordance with past 
experience. A concept like * man ' or ' justice ' is still 
more obviously a thought or judgment construction. As 
expressed in words, it may be said to be an embodiment of 
a judgment or a group of judgments. 

And, in the second place, it is from thdse percepts and 
concepts that new judgments proceed. In other words, 
the basis of our thought in going on to the discovery of 
new facts and relations is what we already know. But 
what we already know at any time is summed up in the 
ideas we possess, that is, in the percepts and concepts which 
have been formed by previous acts of judgment, and em- 
bodied in names. In the development of our knowledge, 



§ II. Perception^ Conception^ and Judgment 47 

however, we are constantly discovering that our knowledge 
on this or that point is unsatisfactory. The old way of 
thinking is perhaps too vague and indefinite to furnish us 
with a satisfactory rule of action, or it may be perceived 
to be inconsistent with new facts that have arrested our 
attention. Indeed, the inadequacy of the habitual, accepted 
point of view may be forced upon us in a variety of ways. 
Frequently, no doubt, the occasion is furnished by some 
practical necessity of action. Necessity is oftentimes the 
mother of invention, and the spur to the discovery of new 
theories and conceptions. In other cases the stimulus to 
criticise our old conceptions may come from social inter- 
course; the conflict of our views with those of people with 
whom we converse, or whose opinions we read, first arouses 
us from our dogmatic slumber. More rarely, perhaps, in 
the case of ordinary minds, theoretical interest may be 
aroused without any external occasion, and the desire for 
truth and consistency may itself be sufficient . to lead one 
to reexamine and transform one's old ideas. Whatever the 
stimulus, thinking is, on one side, a process in which 
old conceptions are recast, and accepted truths transformed, 
a constant process of change in which the old conceptions 
are superseded and destroyed. The old terms, both per- 
cepts and concepts, which form the starting-point are re- 
constituted through a new act of judgment. From one 
point of view, then, it may be said that, hke Saturn, thought 
exists by devouring its own children. But there is another 
side. Thinking is a process of conservation as well as of 
transformation. The old ideas are not entirely destroyed 
and displaced by the new judgment, but further developed 
and defined. The truth which they contain is taken up 



48 The Syllogism and its Parts 

and preserved in the later judgment or series of judgments. 
Moreover, as we have seen, the results of these judgments 
are again laid down as new thought -contents embodied in 
language, and these, in their turn, form the starting-point 
for further judgments. These two aspects or moments of 
thought, then, — what we have called the transforming 
and the conserving functions, — mutually presuppose and 
imply each other. They are not distinct and independent 
mental operations, but organically related moments or 
phases in the life of thought. Perceptions and conceptions 
can arise only through judgments, while judgments pre- 
suppose perceptions and conceptions as their necessary basis 
I and starting-point. Thus the total movement of the whole 
\ thought-process is rightly described as Judgment. 



CHAPTER IV 

THE VARIOUS KINDS OF TERMS 

§ 12. Singular, General, and Collective Terms, — A logical 
term, as we have already seen, is any word or group of words 
which can be used as the subject or predicate of a proposi- 
tion. It is only in propositions, and as elements of propo- 
sitions, that terms have any assignable meaning. It will 
be impossible, therefore, to fix the meanings of isolated 
terms without reference to the way in which they are used 
in propositions. In dealing with terms apart from propo- 
sitions, we shall be concerned mainly with different classes 
of words and the meanings which they usually express. 

The first division which we have to notice is that into Sin- 
gular or Individual, General, and Collective terms. 

(i) A Singular or Individual term is one which can be 
applied in the same sense to but a single thing. The main 
purpose of Singular terms is to refer to, or identify, some thing 
01 experience which can be regarded as a single existence. 
Proper names are all singular. It is true that proper names 
are sometimes used to denote a class of objects, as e,g., ^ a 
Daniel,' ' a Mephistopheles.' But, when thus employed, 
they lose their real character as proper names. That is, 
their function is no longer merely to identify certain indi- 
viduals by naming them, but to describe them by mentioning 
certain qualities or characteristics which they are supposed 
to possess. But the ordinary purpose in using a proper 

E 49 



50 The Various Kinds of Terms 

name is to indicate some individual to whom the name 
belongs. In this sense, then, proper names are Singular. 

In addition, any word or group of words which is applied 
to a single thing may be regarded as singular. And by 
' single thing,' we mean anything which is thought of as 
one, as well as objects which are perceived through the 
senses. Thus, / the waterfall just below the bridge,' ' the 
thought of the present moment,' are singular terms, and so, 
also, are words like ' justice,' ' goodness,' ^ the chief end of 
man.' It is perhaps more doubtful whether we should call 
terms such as ^ whiteness,' ^^ sweetness,' singular, since we 
speak of different degrees and kinds of whiteness and sweet- 
ness. The question would have to be decided in every 
case by reference to the way in which the terms are employed 
in propositions. 

(2) A General term is a name which is capable of being 
applied to a whole group of objects. It is not limited, like 
the singular term, to a single thing, but can be used in the 
same sense of an indefinite number of units. All class 
names, like ^ metal,' ' man,' ^ works on logic,' are of this 
character. Thus a general name is one that refers to a group 
which may be divided into smaller groups, or into individual 
units. Thus iron, gold, silver, etc., are ' metals,' and 
A, B, and C, ' men.' 

A Collective term, on the other hand, is a name applied 
to a number of individual things when taken together and 
treated as a whole, as ' an army,' ^ an audience.' It is 
important to distinguish carefully between general and 
collective terms. A general term is a name which applies 
equally to each individual of the group ; or, in other words, 
it is used of the individuals distributively, A collective 



§ 13- Abstract and Concrete Terms 51 

name belongs to the whole, but not to the separate parts of 
the whole. Thus we say that ^ soldier ' is a general name, 
and is used distributively of each man in a regiment. ^ Regi- 
ment,' however, is a collective name, for it applies only to 
the whole group, and not to the individual soldiers. 

Ambiguity sometimes arises from the fact that the English 
word ' all ' is used in both of these senses. That is, it may 
mean ^all taken together' or ' each and every.' Thus we 
can say: ' All the angles of a triangle are less than two 
right angles,' and ^ All the angles of a triangle are equal to 
two right angles.' In the former sentence, the word ^ all ' 
is used distributively, in the latter collectively. In Latin 
two different words are used: cuncti expresses the collective 
sense of ^ all,' and omnes its distributive signification. 

It is worth noticing in this connection that it is the use which 
is made of terms, rather than the form of the words composing 
them, which determines their logical character. Thus terms which 
are collective in one connection may be general in another. * Regi- 
ment, ' for example, is a collective term with reference to the soldiers 
which compose it, but general when used as a common term for a 
number of similar divisions of an army. The same is also true of 
terms like ^ grove,' ^mob,' ^ class,' etc. Again, collective terms 
may be very properly regarded as singular when the proposition 
in which they are used emphasizes the unity and solidarity of the 
group. A proper name is sometimes applied to a collection of in- 
dividuals that are permanently united or that have acted together 
on some historic occasion, as, for example, ^ The Fifth Cavalry Regi- 
ment,' *The Charge of the Six Hundred.' 

§ 13. Abstract and Concrete Terms. — Terms are fur- 
ther divided into abstract and concrete terms. The word 
* abstract ' i^ pften used popularly to describe anything 



52 The Various Kinds of Terms 

which is difficult to understand. Etymologically, it signifies 
drawn off, separated (ahstraho, to draw off, take away). 
We may distinguish two senses in which the word is used, 
both, however, being derived from its etymological signifi- 
cation. 

(i) A term is called abstract when it refers to some thing 
which cannot be directly perceived through the senses, 
or otherwise directly experienced as an individual object 
or state, and concrete when such form of experience is pos- 
sible. Thus ' a beech tree,' ^ a tall man,' ' a sweet taste,' 
being names of things which can be perceived, are concrete. 
Words like ^ sweetness,' ' hardness,' etc., have no objects 
of immediate experience corresponding to them, and are for 
this reason called abstract. The same is true of terms like 

* individuality,' ' equality,' ^justice,' etc. These words repre- 
sent objects of thought, rather than objects that are directly 
experienced. There may be cases or instances of ' equality,' 

* justice,' etc., which fall under our perception, but the 
real object to which these words correspond is not a thing 
which can be perceived through the senses at all. Their 
reality is conceptual, or for thought, not something directly 
revealed through the senses. 

It is important to notice that there are degrees of abstractness in 
terms, according as the objects for which they stand are nearer to, or 
farther removed from, ordinary sense-perception. All general or 
class names are abstract. One cannot point to a single object to 
which the term ^ metal, ' for example, or the term ' man ' corresponds. 
But although such terms have no direct sensuous object, yet we feel 
that they stand nearer to sense-perception, and are therefore less 
abstract than words like 'animal,' 'inorganic substance.' These 
terms, again, are perhaps less abstract than 'energy,' or 'spirit/ 



§ 13- Abstract mid Concrete Terms 53 

or even than singular terms like ^justice/ ^the ground of the uni- 
verse/ etc. 

(2) Again, the word ' abstract ' is applied to any object 
which is treated apart from the whole to which it belongs. 
Thus it would be an abstraction to attempt to represent 
the nature of a leaf in complete isolation from the plant 
to which it belongs, or to consider the nature of a man 
without regard to the social institutions — family, church, 
state, etc. — of which he is a member. Of course, it is 
essential when dealing with a complex whole to analyze 
it into its parts, and to understand just what is the nature 
of each part when taken by itself. But, in order to compre- 
hend fully the nature of the parts, it is necessary to restore 
them to their proper setting, and to see their relation to the 
concrete whole. In this sense of the word, then, ^ abstract ' 
applies to what is taken out of its proper setting, broken 
off, and considered apart from the things to which it is 
organically related. Concrete, on the other hand, means 
what is whole and complete, a system of things which 
mutually support and explain one another. 

Since science has to analyze things into their elements, 
and to investigate and describe these elements in detail, 
it is impossible entirely to avoid abstraction. But it is 
necessary, in order completely to understand the nature 
of a complex object, that the abstractions of analysis shall 
be corrected. In other words, the concrete relations in 
which things stand must not be ignored in investigating 
them. The conception of evolution in recent times has 
done much to render the biological sciences more concrete 
in the sense in which we are now using the term. For it 
has substituted for the old method of treating each species 



54 The Various Kinds of Terms 

of plant and animal as distinct and separate, ^ cut off from 
each other as if by a hatchet/ the view that all organic 
beings are members of one family, and can be properly un- 
derstood only in their relations to one another (cf. pp. 74-75). 

It is interesting to notice that, from this point of view, sense- 
perception is more abstract than thought. For the senses represent 
things in isolation from each other. Each thing is known in sense- 
perception as a separate individual, occupying its own space and 
time, and, in this way, cut off from its fellows. It is the business of 
thought, on the other hand, to discover the relations between things, 
and the principles according to which they are united. Thinking 
thus overcomes the abstract point of view of sense-perception by 
showing that what appear to the latter as separate objects are 
really closely and necessarily connected as members of a com- 
mon unity or system. Each science takes as its province certain 
facts which resemble one another, but which nevertheless appear 
to sense-perception to be quite independent. It attempts by 
thinking to bring these facts into relation, to show that they are 
all cases of some law, that there is a common principle which unites 
them as parts of a whole or system. The law of gravitation, for 
example, expresses the unity which thought has discovered in 
things which appear to sense-perception as different as the falling 
of an apple, the movements of the heavenly bodies, and the ebb 
and flow of the tides. Scientific knowledge, then, is more con- 
crete than the facts which we learn from ordinary sense-percep- 
tion, because it brings to light real unity and connection in facts 
which appear to be entirely isolated and independent from the 
latter point of view. 

In employing the terms ' abstract ' and ^ concrete ' it 
is of the utmost importance to distinguish the two signifi- 
cations of the words. From one point of view, as we have 
seen, all thought terms are abstract, as opposed to words 



§ 14- Positive and Negative Terms 55 

which refer directly to objects of sense-perception. In 
another sense, ' abstract ' denotes what is partial and incom- 
plete, what is taken by itself and out of relation to the system 
of things to which it belongs. And, since the real connection 
and relations of things are not given by perception, but 
have to be discovered by thought, the knowledge which the 
latter yields is more concrete, in this latter sense of the term, 
than that afforded by the former. 

§14. Positive and Negative Terms. — The distinction 
between Positive and Negative terms is very obvious. Posi- 
tive terms express the existence of some quality, or group 
of qualities, in the objects which they denote; as, e.g,^ 
^ happy,' ^ good,' ^ equality,' ' organism,' etc. A Negative 
term, on the other hand, indicates the absence of qualities 
or properties in some object; ' bad,' ^unhappy,' ' inorganic,' 
injustice,' for example, are negative terms. Negative 
terms are often formed from positive by means of the affix 
less^ as in ^ hopeless,' or by means of certain prefixes, of 
which the more common are un^ in, dis, a, anti. Words 
which are positive in form are, however, often negative 
in meaning, and are used as the contradictories of other 
terms. Thus ' ignorant ' is generally regarded as the nega- 
tive of ^ learned,' ^ darkness ' is the negative of 'light,' etc. 
It is not always possible, however, to find a separate word 
to express the exact opposite of every positive term. Words 
are used primarily to express the presence of qualities, and 
the negative idea may not be referred to so frequently as 
to require a separate word to express it. Thus there is no 
independent term to express the opposite of ^ transferable,' 
but by employing ' non ' as a negative prefix we obtain 
' non-transferable.' 



56 The Various Kinds of Tej^ms 

It is always advisable when we wish to limit a term strictly to its 
negative application to employ not or non as a prefix. Words 
which are negative in form frequently have a more or less definite 
positive signification. Jevons points out that words like ^unloosed' 
and ^ invaluable/ though negative in form, have a positive meaning. 
But, in addition, terms like ^unhappy,' ^immoral,' do not merely 
indicate the absence of positive qualities, but also express some 
positive properties of the objects to which they are applied. We 
speak of a person 'being positively unhappy'; and we employ 
'non-moraP to express the simple negative relation rather than 

* immoral.' 

On the other hand, there are certain terms which are positive in 
form that express the absence of qualities or attributes. Words like 

* blind,' 'dumb,' ' maimed, ' orphaned,' may be given as examples. 
These are often called Privative terms, rather than Negative, the 
distinction being that they refer to qualities or attributes which the 
objects to which they are applied naturally and usually have, but of 
which they have been deprived, or which they have never possessed. 
Thus ' blind,' as applied to a man, implies that he has lost, oris desti- 
tute of, the ability to see which naturally belongs to a human being. 

Again, other terms seem to be positive and negative solely in 
relation to each other. ' Element ' and ' compound ' are related as 
negatives or contradictories. It is difiicult, however, to say which 
term is in itself negative or positive. 

It is important to notice the distinction between the 
relation in which positive and negative terms stand to each 
other, and that expressed by words which have to do with 
opposite extremes of something which possesses quality 
or degree. Positive and negative terms are mutually 
Contradictory. An element is what is not a compound, 

* dishonest ' is the contradictory of ' honest,' and as con- 
tradictories there is no middle ground between them. What 



§ 15- Absolute and Relative Terms 57 

is not an element is a non-element or a compound. Con- 
trary terms, on the other hand, express a great difference 
of degree in the objects to which they refer. Thus ^ foolish ^ 
is the opposite of ^ wise,' ^ cold ' the opposite of ^ hot,' and 
' bitter ' of ^ sweet.' But there is always the possibility of 
a middle ground between opposites. We cannot say that 
a man must be either wise or foolish, a taste either sweet 
or bitter. The logical contradictory of ' wise ' is ^ not-wise/ 
of ^ bitter ' is ^ not-bitter,' etc. Contrary terms, then, 
must be carefully distinguished from contradictories, and 
we cannot conclude because one contrary term is false in 
a given case that the other is necessarily true (cf. § 25). 

§15. Absolute and Relative Terms. — Another classi- 
fication of terms, which is usually given by logicians, is 
that into absolute and relative terms. An Absolute term 
is one which refers to an object which exists by itself, and 
has an intelligible meaning when taken alone. Thus ^tree,' 
^ house,' 4he State of New York,' are examples of absolute 
terms. A Relative term, on the contrary, is a name which 
only derives a meaning from its relation to something else. 
The term ^parent,' for example, cannot be thought of except 
in relation to 'child.' Similarly, 'teacher' is relative to 
'pupil,' and 'cause 'to 'effect.' Relative terms usually go in 
pairs and are known as Correlatives. Adjectives, as well as 
nouns, may be related in this way. The presence of one 
quality or characteristic in a thing frequently implies the 
presence of others. Thus, ignorance and superstition, 
sympathy and tolerance, are necessary correlatives, because 
the one involves the other, or is invariably connected with it. 

It is, of course, true that no finite thing is completely absolute or 
independent of other things. The nature of each thing is largely 



58 The Various Kinds of Terms 

determined by the nature of the other things with which it stands 
in relation. A tree, for example, is relative to the seed from which 
it sprang, the soil in which it grew, the sunshine, rain, etc., which 
accompanied its growth. All finite things have a beginning and an 
end, and are also influenced throughout the whole period of their 
lives by the action of other things. They are, therefore, not com- 
pletely absolute or independent. It is, however, possible to make a 
distinction between words which are the names of things that are 
comparatively independent, and may for ordinary purposes be con- 
sidered by themselves, and those which have only a meaning when 
regarded as correlatives. 

§ 1 6. Extension and Intension of Terms. — In the fore- 
going sections of this chapter we have explained the main 
distinctions which concern the various kinds of terms with 
which logic deals. It is now necessary to notice two different 
purposes for which terms are employed. In the first place, 
terms are used to refer to things, to name and identify 
them. Thus ^ man ' refers to the different individual men, 
John Smith, Thomas Brown, etc., as well as to the various 
classes of men, Caucasians, Indians, Mongolians, etc. As 
denoting or naming objects, whether these be individual 
things or classes of things, terms are said to be employed 
in Extension. But words are also used to describe as well 
as to name. That is, they represent the qualities or attrib- 
utes belonging to things for which they stand. They are 
not bare names without signification ; but, as the expression 
of ideas, they stand for certain qualities or characteristics 
which things are judged to possess. 'Man,' for example, 
is not merely a name which may be applied to individual 
human beings or races of men ; but it implies that the objects 
so named have certain qualities, such as animal life, reason. 



§ 1 6. Extension and Intension of Terms 59 

and the power of communicating with their fellows. When 
words are used in this way to define or describe things, 
rather than merely to name them, they are said to be em- 
ployed in Intension. 

The terms ^Denotation' and ^ Connotation ' were used by Mill 
instead of Extension and Intension, respectively, and have been 
adopted pretty generally since his time. To /denote' is to point 
out or specify the objects for which a term stands ; and to ^connote ' 
is to take account of the attributesorjqualities which a name implies. 
The words ' depth ' and ^ range ' are also sometimes used as synony- 
mous with Extension, and * breadth ' or ^ comprehension' instead^of 
Intension. The terms to be remembered, however, are Extension 
or Denotation, and Intension or Connotation. 

It is useful to accustom ourselves to distinguish these 
two functions or uses of a term, — to notice, that is, the 
things or classes of things to which the name applies, 
and also to reflect upon the signification, or ways of judg- 
ing about these things, for which the name stands. The 
Extension of a term, as has been said, indicates the objects 
to which a name applies, and the Intension the qualities 
or attributes which it signifies. From the point of view of 
extension, therefore, ^ planet ' may be defined by mentioning 
the names of the various planets. Mercury, Venus, the Earth, 
Mars, etc. Similarly, a term like ^carnivora' might be given 
in extension by naming seals, bears, weasels, dogs, wolves, 
cats, lions, etc. Usually, however, we define from the point 
of view of intension, that is, by stating the qualities or char- 
acteristics for which the term stands. Thus we give the 
intensive meaning of ^ planet,' as a heavenly body which 
revolves in an elliptical orbit around the sun. ^Carnivora,' 
defined from the same point of view, are mammalian verte- 



6o The Various Kinds of Terms 

brates which feed upon flesh. It is not unusual, however, to 
supplement an intensive definition by turning to extension and 
enumerating examples. Thus we might add to the definition of 
' carnivora ' just given the words, ' as lions, tigers, dogs,' etc. 
It is sometimes said that the intension and extension of terms 
vary inversely. This is simply an attempt to give a mathemati- 
cal form of statement to the fact that the more a term is defined, 
or limited, by the addition of attributes, the fewer are the 
objects to which it applies. ^As the intension of a term is 
increased, its extension is diminished, and vice versa^^ is the 
form in which the relation is often stated. For example, let 
us begin with some class name like ' animal,' which has a 
great extension, and add a new attribute, ^rational.' We 
get ' rational animal ' = man. This term now applies to 
a much smaller number of individuals than ^ animal.' The 
extension of the former term has been diminished, that 
is, by increasing the intension. If we add to ^ man' still 
another attribute like ' white,' we again lessen the number 
of individuals to which the term applies. In general, then, 
it can be seen that the extension of a term is lessened as it 
is made more definite by the addition of new attributes. 
And, conversely, by stripping off attributes, by ' decreasing 
the intension,' the number of individuals to which a term 
applies is increased. There is, however, no exact ratio 
between the increase or decrease of intension and the corre- 
sponding change in extension. Indeed, the extension of a 
class may increase greatly without any loss of intension on 
the part of the term by which the idea is expressed. Thus 
the meaning or intension of the term' ' man' has not lost, 
but rather gained, during the last hundred years by the in- 
crease of population throughout the world. 



§ 1 6. Exte7tsion and Intension of Terms 6 1 

In general, it is only when some kind of a formal clas- 
sification is instituted, when terms are taken as arranged in 
order of subordination, that there is any meaning in speak- 
ing of their extension and intension as in inverse relation. 

Extension and intension, according to the view just given, 
represent two different uses or functions of terms. Every 
term denotes some object or group of objects more or less 
directly, and at the same time connotes or signifies certain 
qualities or attributes. Sometimes the one purpose, some- 
times the other, is the predominant one. Proper names, 
for example, are used primarily to denote or mark out 
things, and do not directly qualify or describe them. In 
the proposition, ^ these animals are all vertebrates,' the 
predicate term ' vertebrates ' is employed less as a name of 
a number of animals than as a description of their qualities. 
Nevertheless, in both these cases the terms employed have the 
double function of naming or denoting objects, and of con- 
noting qualities. 

Mill, however, and certain other logicians who follow 
him, seem to make an absolute distinction between con- 
notative and non-connotative terms. '^ A non-connotative 
term is one which signifies a subject only, or an attribute 
only. A connotative term is one which denotes a subject, 
and implies an attribute. By a subject is here meant any- 
thing which possesses attributes. Thus ^John,' or ^Lon- 
don,' or * England,' are names which signify a subject 
only. ^Whiteness,' Mength,' Wirtue,' signify an attribute 
only. None of these names, therefore, are connotative. 
But 'white,' Mong,' ' virtuous,' are connotative. The word 
' white ' denotes all white things, as snow, paper, the foam 
of the sea, etc., and implies or, in the language of the school- 



62 The Various Kinds of Terms 

men, connotes the attribute whiteness, ... All concrete gen- 
eral names are connotative. The word ^man/ for example, 
denotes Peter, James, John, and an indefinite number of 
other individuals, of whom, taken as a class, it is the name. 
But it is applied to them because they possess, and to signify 
that they possess, certain attributes." ^ 

There is no real ground, I think, for such an absolute 
distinction between connotative and non-connotative terms, 
or, as we may call them, descriptive and non-descriptive 
terms. Of course, it is true that some terms are more directly 
descriptive than others; but when we consider the use or 
function of terms, we find that they are never used merely 
to name things, or merely to connote attributes, though in 
certain cases the former purpose is the primary one, and 
in other cases the latter object is more prominent. Even 
when proper names are employed, the qualities or character- 
istics of the objects named are indirectly implied. The very 
fact that a proper name is given to an object implies that 
it possesses a certain definitely marked individuality. More- 
over, a proper name when used intelligently carries with it some 
still more definite information regarding the qualities of the 
thing to which it is applied, as, for example, whether it is a 
name of a person, an animal, or a place. And, on the other 
hand, every term has an application to real objects, and so 
a denotation, though this reference to reality is often indirect 
and somewhat indeterminate. For, without the assumption 
of this application, no term could be a part of an intelligible 
proposition or represent a genuine thought. Every term, then, 
more or less directly, both denotes objects and connotes 
attributes. 

» Mill, Logic, Bk. I., Ch. II., § 5. 



§ 1 6. Extension and Intension of Terms 63 

REFERENCES 

J. S. Mill, Logic, Bk. I., Ch. II. 
F. H. Bradley, The Principles of Logic, pp. 155-173. 
B. Bosanquet, Logic, Vol. I., pp. 46-71. 
" " The Essentials of Logic, Lecture V. 

J. N. Keynes, Studies and Exercises in Formal Logic, 4th edition, 
Part I., Chs. I. and II. 



CHAPTER V 

DEFINITION AND DIVISION 

§ 17. Fixing the Meaning of Terms. — We have already 
referred to the necessity of definitely fixing the meaning of 
the terms which we employ in reasoning. In ordinary 
life, words are frequently used in a loose and shifting way, 
without any clear conception of the qualities or properties 
which they connote, or of the objects to which they apply. 
Logic demands, in the first place, that we shall have clear 
and precise ideas corresponding to our words, and that the 
signification and scope of the latter shall be carefully deter- 
mined. But this is a demand to which little attention 
is paid in the ordinary affairs of life. To define our terms 
in explicit language, or even to make clear to ourselves 
the ideas and things for which they stand, is by no means a 
natural or a universal mode of procedure, but something 
which requires a distinct, conscious effort. 

Bacon, Hobbes, Locke, Hume, and nearly all of the 
older philosophical writers have warned us against the abuse 
of words. The whole matter has been expressed very clearly 
by Locke, from whom I quote the following passage: — 

^^ For he that shall well consider the errors and obscurity, 
the mistakes and confusion, that are spread in the world 
by an ill use of words, will find some reason to doubt whether 

64 



§17. Fixing the Meaning of Terms 65 

language, as it has been employed, has contributed more 
to the improvement or hindrance of knowledge amongst 
mankind. How many are there, that, when they would think 
on things, fix their thoughts only on words, especially when 
they would apply their minds to moral matters; and who, 
then, can wonder if the result of such contemplations and 
reasonings about little more than sounds, whilst the ideas 
they annex to them are very confused and very unsteady, 
or perhaps none at all; who can wonder, I say, that such 
thoughts and reasonings end in nothing but obscurity and 
mistake, without any clear judgment or knowledge ? 

^^This inconvenience in an ill use of words men suffer 
in their own private meditations; but much more manifest 
are the discords which follow from it in conversation, dis- 
course, and arguments with others. For language being 
the great conduit whereby men convey their discoveries, 
reasonings, and knowledge, from one to another; he that 
makes an ill use of it, though he does not corrupt the foun- 
tains of knowledge, which are in things themselves, yet he 
does, as much as in him lies, break or stop the pipes whereby 
itns distributed to the public use and advantage of mankind." ^ 

The remedy for the obscurities and confusions of words is 
to be found in clear and distinct ideas. We must endeavour 
to go behind the words- and realize clearly and distinctly 
in consciousness the ideas for which they stand. Now the 
means which logic recom^mends for the attainment of this 
end is definition. The first requirement of logical reasoning 
is that terms shall be accurately defined. There are, however, 
two ways in which the meaning of a term may be defined 
or explained. Every term, as we have already seen (§ 16), 

^ Essay concerning Human Understanding, Bk. III., Ch. XI. 

F 



66 Definition and Division 

may be regarded either from the point of view of intension, 
or from that of extension. To define, in the usual sense, 
is to explain from the standpoint of intension, to state the 
attributes or qualities which are connoted by the term. The 
process of explaining terms with reference to the objects, 
or classes of objects, for which they stand is known as Divi- 
sion. We may include, then, under the general term defini- 
tion, (i) Intensive definition^ or definition in the ordinary 
sense, and (2) EoUensiv-e-definition -or division. 

§ 18. Definition. — To define a term is to state its con- 
notation, or to enumerate the attributes which it implies. 
Thus we define a parallelogram as a quadrilateral figure 
whose opposite sides are parallel. A distinction is often 
made between verbal and real definition. When we merely 
wish to explain the meaning in which we intend to employ 
some term, we have verbal definition. But when it is the 
purpose of our assertion to state the real nature or essential 
characteristics of some object, the proposition employed is 
said to constitute a real definition. This distinction, though 
not without importance, cannot, I think, be regarded as 
ultimate. For we never define a word or term for its own 
sake merely, but in order to understand the nature of the 
objects to which it refers. Indeed, a mere word, apart 
from its uses, or from the things for which it stands, has no 
interest for us. In defining a term, then, we are always 
attempting to explicate or explain, more or less directly, 
the nature of a thing, or our idea about a thing. 

Nevertheless, there is an advantage in distinguishing 
propositions whose immediate purpose is to expound the 
meaning of a word, from those which assert something 
directly of an object. ^Monarchy consists in the authority 



§ 1 8. Definition 6/ 

of one man over others,' may be regarded as a verbal defini- 
tion, because the purpose of the proposition is simply to explain 
the meaning of the subject term. On the other hand, ' iron is 
malleable ' is a real definition (though not a complete one), 
because it does not primarily refer to the signification of the word 
'iron/ but to the real object to which the name is applied. 

In this connection, it is interesting to notice that a proposition 
which amounts to nothing more than a verbal definition, is some- 
times put forward as if it were an assertion which contained some 
real knowledge. The solemn commonplaces in which ignorant per- 
sons delight are often of this character. 'A republic is a govern- 
ment by the people,' ' a just man will do what is right,' ' if it rains, 
the ground will be wet,' may serve as examples. The mistake in 
such cases consists in supposing that these assertions are anything 
more than verbal. '^ Trifling propositions," is the name that 
Locke gives to this form of statement. ' The property of water 
is to wet, and fire to burn; good pasture makes fat sheep, and a 
great cause of the night is the lack of the sun,' are Corin's pro- 
found remarks to Touchstone, in summing up his philosophy. 

There are two points of view from which the subject 
of definition may be considered. We might either discuss 
the best method of obtaining real definitions of the nature 
of things, or might confine our attention to the requirements 
which a good definition has to fulfil, A person's ability to 
define either a term, or the thing for which the term stands, 
depends, however, upon the possession of clear and distinct 
ideas on the subject. The problem, then, as to the best 
method of finding definitions, resolves itself into an inquiry 
concerning the means to be used in obtaining and classi- 
fying our ideas in general ; and the answer to this question, 
so far as an answer can be given, must be found in the theory 



68 Definition and Division 

of logic as a whole. In our treatment of the subject we shall, 
therefore, confine our attention mainly to a consideration 
of the requirements of a logical definition, and the rules 
which must be observed in stating it in language. 

Before entering upon the subject, however, it is interesting 
to refer briefly to the method proposed by Socrates for obtain- 
ing definitions. Socrates, as we have already seen (§ 5), was 
the first to emphasize the necessity of defining and fixing the 
meaning of familiar terms. He found that, though the people 
of Athens were constantly using terms like ' good,' 'beautiful,' 
' justice,' and ' temperance,' none of them, not even those with 
the greatest reputation for wisdom, were able to give any clear 
and consistent statement of what these terms implied. Soc- 
rates himself did not profess to be wiser than the rest, but he 
had a genuine spirit of inquiry, and made it the business of his 
life to try to arrive at clear conceptions, especially with regard 
to certain fundamental ethical virtues, like justice, and tem- 
perance, and wisdom, which he regarded as of the utmost 
practical importance. It was by means of conversation with 
others that he sought to gain clear ideas regarding the nature 
of these virtues. By a series of questions and answers, by com- 
parison of any definition proposed with particular facts which 
are admitted, he led his interlocutors to expose and refute the 
inadequacies of their earlier statements. 

This method of proceeding by means of question and 
answer, and thus compelling a speaker to admit particular 
facts which refute the general thesis which he is maintaining, is 
called Dialectic. This was the means by which Socrates con- 
stantly strove to advance to consistent and adequate defini- 
tions. Apart from the dialectical and dramatic form which the 
Socratic argument took, the method employed is essentially 



§ 1 8. Definition 69 

that of induction. For the definition, or conception, is derived 
from a comparison of particular instances, both positive and 
negative. By a consideration of individual cases, Socrates 
sought to obtain a definition which would be a complete and 
adequate expression of the nature of all the individuals which 
share in the class name. Aristotle says that it is to Socrates 
we owe the method of induction and logical definitions. 
Clear and distinct conceptions, formulated in exact definitions, 
constituted the scientific goal for Socrates, and the inductive 
procedure of observing and classifying particular instances 
was the means which he employed for reaching this goal. 
It should, however, be added that the Socratic use of in- 
duction, as Plato represents it in his Dialogues, is more often 
popular in character than strictly scientific, judged by our 
present standards. 

The second question has reference to the formulation of a 
definition in language. Suppose that we already possess a clear 
conception of the meaning of the terms to be defined, what are 
the conditions which a logical definition must fulfil? The 
answer to this question is usually given in logical text-books 
by means of a set of rules for definition. Before stating these 
rules, however, it is necessary to explain the meaning of the 
terms ' genus ' ^ species,' and ^ differentia,' which will be fre- 
quently employed throughout the remainder of this chapter. 
These terms, together with ^ property ' and ' accident,' consti- 
tute what the older logicians called the Predicables, and state 
all the possible relations which a predicate may express with 
regard to a subject. It will only be necessary, however, for 
us to consider briefly the signification of the first three terms. 
In logic, any term may be regarded as a genus which con- 



70 Definition and Division 

tains two or more subordinate classes or species. A species, 
on the other hand, is simply a subdivision or subordinate 
class of some larger whole. Thus ' metal ' is a genus with 
reference to iron, gold, silver, etc., which are its species. 
' Rectilinear figure ' is the genus to which belong the various 
species, triangle, quadrilateral, pentagon, etc. The differentia 
of any term is made up of the qualities or characteristics which 
distinguish it from other terms, from the genus to which it 
belongs, as well as from the species which are coordinate with 
it. Thus the logical differentia of a triangle is the property of 
having three sides ; the differentia of man is that which dis- 
tinguishes him from other animals, whether this be the power 
of speech and reason, or some other characteristic, either physi- 
cal or mental. 

The use of the terms ' genus ' and ' species ' in logic is en- 
tirely relative. That is, any term may be considered either 
as a species or a genus, according as it is regarded as form- 
ing a part of some more comprehensive class, or as itself 
including other classes. Thus man, for example, is a species 
of the genus ' animal ' ; but the same term also may be 
regarded as a genus including various species of men, Cauca- 
sians, Negroes, Mongolians, etc. In the same way, ' animal ' 
may be considered a species of the still more comprehensive 
class ' organized being,' and this latter term again as a species of 
the genus ' material being.' A still higher or more comprehen- 
sive term which includes as its species material and spiritual 
beings alike is ' being.' Since this term includes everything 
which exists, and can therefore never be included in any more 
general class, it is sometimes called the highest genus {sum- 
mum genus). On the other Hand, we might proceed down- 
wards until we come to a class which does not admit of division 



§ 1 8. Definition 71 

into any subordinate classes. Such a term is called in logic 
the lowest species {infima species). 

It is important to notice that the terms ' genus ' and ' species ' have 
not the same signification in logic as in the natural sciences. In 
classifying objects in natural history, we use the terms * variety/ 
' species/ ' genus/ ' family/ and ^ order/ to denote varying degrees of 
relationship between certain groups or classes of objects. These 
terms, as thus employed, also indicate certain relatively fixed divi- 
sions, or permanent ways of grouping the various forms of plant and 
animal life. But in logic the terms * genus' and ^species' are em- 
ployed to indicate the relationship between any higher and lower 
class whatsoever. Moreover, as we have seen, any term (excepting 
only the highest genus and the lowest species) may be regarded 
from different standpoints, as either a genus or a species. 

We shall now proceed to state the requirements of a logical 
definition : — 

(i_) A definition should state the essential attributes of the thing 
to be defined. This is done by stating the genus to which the 
object belongs, and also the peculiar marks or qualities by 
means of which it is distinguished from other members of the 
same class. Or, as the rule is usually stated : A logical defini- 
tion should give the next or proximate genus, and the differ- 
entia of the species to be defined. Thus we define a triangle 
as a rectilinear figure (genus) having three sides (differentia) ; 
and man as an animal (genus) which has the power of speech 
and reason (differentia). 

(2) A definition should not contain the name to be defined, 
nor any word which is directly synonymous with it. If, for 
example, we were to define justice as the way of acting justly, 
or life as the sum of vital processes, we should be guilty of a 
violation of this rule. 



72 Dejinitioii ajid Division 

(3) The dijlnilion should he exaetJy equivalent io Ihe ejass of 
ohjee/s defined ; tJiat is, it must be neither too broad nor too narrow. 
\\\ other words, llio dcfinilion must take account of the whole 
class, and nothing hut the ehiss. 'A sensation is an elementary 
state of consciousness,' for example, is too broad a definition, 
since it a])i)lies equally to affective and conative elementary 
processes. On the other hand, the definition of government 
as 'an institution created by the people for the protection of 
tlieir lives and liberties,' is too narrow. For it takes no 
account of absolute forms of government which do not depend 
upon the will of the i)eopIe. Each of these cases may be 
regarded as a failure to give the true differentia of the class 
to be defined, and hence as violations of the first rule. 

(4) .1 definition sliould not be expressed in obscure, figurative, 
or ambiguous lano^uage. The reasons for this rule are at once 
evident. Any lack of clearness or definiteness in a definition 
renders it useless as an explanation. Sometimes the words 
used in defining may be less familiar than the term to be ex- 
plained {ii^ju^tuni fxi' ii^notius). The definition which was 
once gi\'en of the word ' net ' as ' a reticulated texture with 
large interstices or meshes,' may serve as an example. 

(5) .1 definition sjioutd, wJienever possilde, be affirmative, 
rattier tlian nei^ative. A definition, that is, should state 
what a term implies, rather than what it does not imply. 
Sometimes, however, tlie purpose of a definition may be best 
attained by a negative statement of what is excluded by the 
meaning of the term. Thus, for example, we may define a 
spiritual being as a being which is not material, that is, unlike 
a material body made up of parts extended in s})ace. This 
is an exception to the rule. But it should be noted that there 
are other definitions which, while negative in form, are not 



§ 1 8. Definition 73 

really exceptions to it. Such, for instance, is the definition of 
a bachelor as an unmarried man. This is a precise statement 
of what is included in the meaning of that term. It is, there- 
fore, the meaning rather than the form of the definition to 
which we should look in applying this rule. The fault against 
which it is directed is that of the so-called 'infinite' definition, 
which merely states what a thing is not, without regard to 
whether such a negation sensibly increases one's knowledge of 
the meaning of the term or not. Such a definition is ' infinite' 
in the sense that to enumerate everything that the term to be 
defined is not would be an infinite process. 

(i) A logical definition, as has been said, requires us to mention 
the proximate genus or next higher class to which the species to be 
defined belongs, and also the specific or characteristic differences 
which distinguish it from other species. Now it is clear that there 
are certain cases in which these conditions cannot be fulfilled. In 
the first place, no logical definition can be given of the highest genus, 
because there is no more general class to which it can be referred. 
And, again, although it is possible to give the differentia of any 
species such as 'man' or 'metal,' it is not possible to state indi- 
vidual characteristics by means of a logical definition. An indi- 
vidual thing may be perceived, and its various properties pointed 
out. But it is never possible to state in a logical definition wherein 
the individuality of a particular thing consists. The uniqueness of 
a particular object cannot be summed up in a general definition, but 
must be learned through perception. We may perhaps say that the 
highest genus is above, and the individual thing below, the sphere of 
logical definition. 

There are, moreover, other terms such as 'space,' 4ime,' ' life,' 
'thought/ which are not readily referred to any higher class, and 
for which, therefore, logical definitions cannot be given. These 
terms are sometimes said to denote objects which are sui generis^ 
or of their own class. 



74 Definition and Division 

(2) This use of 'genus' and 'species' in definitions comes to us 
from the logic of Aristotle. The purpose of definition, as we have 
seen, is to make our conceptions clear and precise; that is, the 
definition should state, as exactly and concisely as possible, the 
essential characteristics of the thing defined. And the most con- 
venient way to do this is often to mention some more inclusive 
group of objects, the general nature of which is known, and at the 
same time to add the special characteristics which distinguish the 
thing in question from the rest of this group. Thus, for example, 
it is much more convenient to define a dicotyledon as ' a plant 
with two cotyledons or seed shoots' than it would be to enumer- 
ate all the special characters of plants as well as the distinctive 
character of the germinating seed. 

(3 ) B ut while this is true in general, it should not be supposed that 
this is the only way in which good definitions can be reached. The 
purposes and methods of the particular science or study employing 
the definition determine both its content and the proper form of its 
statement. The definition, by giving genus and specific differentia, 
is especially useful where our chief purpose is one of classification, 
of ranging the concepts employed in any subject in a fixed order for 
further reference and use. But it is often true, especially in the 
natural sciences, that a thing may be better defined by telling how 
it comes into being than by giving it a place in a fixed scheme of 
classification. This second mode of definition might be called 
genetic definition. Its use is frequent where we are concerned with 
processes and the laws of their action, and it often represents an ad- 
vance in knowledge upon classificatory definition. To define ' heat, ' 
for example, as 'a force in nature recognized in the phenomena of 
fusion and evaporation, etc.,' tells us less about its real nature than 
the statement that it is' a form of energy possessed by bodies derived 
from an irregular motion of their molecules.' To define ' water' as 
' a fluid which descends from the clouds in rain,' is less adequate for 
scientific purposes than the chemical definition of it as * a fluid 



§ 1 8. Definition 75 

formed by adding one part of oxygen to two parts of hydrogen.' In 
zoology and botany the older definitions of animals and plants by 
giving their genus and the distinctive or ' diagnostic ' marks by v^hich 
their respective species might be recognized, received a new meaning 
in the light of the theory of evolution ; for these classificatory relation- 
ships have been shown to be evidences and results of the degree 
of affinity in descent from common progenitors, and are revised 
accordingly. The definition of ^ ape, ' for example, as a ' variety of 
the quadrumana having teeth like man, etc.,' is widened to include 
less obvious characteristics; and this and other similarities to man, 
which the older definition merely stated, are now explained. In 
all such cases, the genetic definition tells us more about the real 
nature of the thing defined, because it relates the thing, through 
general laws of behaviour, to other things and their characteristics. 
Again, there are other cases where either mode of definition seems 
equally adequate in itself, and we can employ them indifferently 
according to the purpose of the moment. In mathematics, for 
example, a circle may be defined equally well as ' a plane figure 
bounded by a line, all points of which are equally distant from a 
point within called the centre,' or as ^ the plane figure generated by 
revolving a straight line about one of its extremities which remains 
fixed.' And, finally, we may mention a class of genetic definitions 
whose value seems merely practical, in that their purpose is only 
to give a brief statement of how to make a certain thing when 
it is wanted. Such are the chemical formulae used in certain 
manufactures, or the ^receipts found in cook books. 

(4) In addition to the question as to which of these modes of 
definition is to be preferred in any case, the further problem arises : 
What are the essential characteristics which the definition must 
state? This also must be determined by the purposes for which it 
is to be used. The essential characteristics of any subject will vary 
widely according to the different points of view from which it is ex- 
amined. The legal definition of ^ insanity,' for example, differs from 



"j^ Definition and Division 

the medical. Jurisprudence is concerned here not with the study 
of mental abnormality as such, but with the determination of that 
degree of it which it is expedient to recognize as constituting irre- 
sponsibility for what would usually be considered as a criminal act, 
or as nullifying contracts, deeds, and wills. And, in general, 
we may say that the purpose of definitions in law is always to 
insure that the original intention of the legislator shall be carried' 
out, by stating as clearly as possible the distinguishing marks 
of the agents, acts, or states to which the law is intended to apply. 
This purpose, and not that of an exact statem.ent of the nature of 
the thing defined, determines what shall be considered essential 
characteristics in its eyes. It is plain that there may often be, there- 
fore, an important difference between a good legal definition and a 
good definition of the same subject-matter in one of the natural 
sciences, for example. This example will also serve to illustrate 
the truth that it is neither necessary nor desirable that all definitions 
should be equally precise. A definition which, from one point of 
view, lacks logical completeness may sometimes be sufficiently exact 
for the purpose on hand. Such is the case, for example, with those 
definitions which are preliminary in any science or argument, and 
serve to outline its field and to prepare the way for further discussion. 
Too great haste in defining is in its way almost as much a fault as 
failure to define at all; and there is a peculiar fallacy which at- 
tempts to bar the way to all fruitful discussion by remarking that ' it 
is all a question of definition, and if the terms had been first defined, 
all this argument would be unnecessary.' The remark is perfectly 
true, but it overlooks the fact that any fully adequate definition is 
the product of thinking, not its point of departure. 

In the general rules of definition, therefore, the terms ^ genus ' and 
* specific differentia ' should be taken in a wide sense. It should be 
remembered that they vary with the purpose of the definition, 
and that that purpose may be either merely to insure recognition by 
the statement of convenient marks or signs, as in the ' diagnostic ' 



§ 1 9- Division yy 

definitions of disease for the use of the physician ; or it may be the 
ordered arrangement of the subject-matter of a science, as sum- 
ming up the knowledge we already have and stating it in convenient 
form for preservation and further investigation; or, again, it may 
be the concise statement of the way in which particular processes 
and objects are explained by the general laws of causation. 
According to these varying purposes, both ^ genus ' and ^ specific 
differentia ' may be sometimes descriptive, sometimes explicative, 
sometimes fixed classes, sometimes genetic processes. 

§ ig. Division. — We have already spoken of Division as a 
process of defining a term from the point of view of extension. 
This is to enumerate the objects or classes of objects which 
the term denotes. This enumeration must, however, be 
guided by certain principles which we have now to consider. 

It is usual to begin this subject by speaking of Dichotomy, 
or the division of a term into two parts (S^%a refivetv^ to cut 
in two). This is a purely formal process, and is based on the 
so-called law of Excluded Middle, which is regarded as one of 
the fundamental laws of thought. This law may be stated as 
follows: There is no middle ground between contradictories. 
Any term, a, is either h or noi-b. A triangle is either equilateral 
or not-equilateral. Of two contradictory predicates, one or 
the other must belong to every possible subject. 

Now it is clear that this is a purely formal principle of divi- 
sion. Some positive knowledge of the particular facts involved 
is always necessary, in order to enable one to determine w^hat 
things do stand in this relation of logical opposition. The 
logical law, in other words, does not help us at all in deciding 
what may be regarded as not-a in any particular case. It is 
not, therefore, a means of increasing our knowledge, but 
merely a principle of order and arrangement. This fact, obvi- 



78 Definition and Division 

ous as it seems, was not understood by the Schoolmen who 
busied themselves with logic in the latter part of the Middle 
Ages. They clung firmly to the belief that it was possible to 
discover the nature of particular facts by purely formal opera- 
tions of this kind. Accordingly, they spent a great deal of 
time in classifying and arranging terms as contradictories, 
contraries, etc. This work was doubtless of much service in 
fixing the meaning of terms, and in preventing confusion 
in their employment. But it was a purely verbal investigation, 
and, of course, could not lead to any discoveries regarding the 
nature of things. 

Moreover, it must be noticed that we do not always get 
propositions to which any meaning can be attached by uniting 
subjects and predicates in this way. If the law of dichotomy 
is not guided by knowledge of the particular facts, it will give 
absurd propositions like ' virtue is either square or not-square,' 
^ iron is either pious or not-pious.' Unmeaning propositions of 
this kind being left out of account, however, we may proceed 
to divide everything according to this principle. All geo- 
metrical figures are either rectilinear or not-rectilinear; all 
rectilinear figures either triangular or not-triangular; all 
triangles, equilateral or not-equilateral, etc. This method of 
division may be represented thus; — 







Substance 

1 




1 
Material 

1 


1 
non-material 


1 

anic 




1 
not -organic 




.1 
Mineral 

1 


1 
not-mineral 


1 
old 




not-gold 



§ 19- Division 79 

If it were desirable, the terms ^non-material/ ^organic/ and 
' not-mineral ' might also be further subdivided in the same 
way. 

Now it is not difficult to see that the practical use of this 
principle will depend upon our ability to find some positive 
value for the negative not-a. That is, to make the law of more 
than formal value, we must know what concrete term excludes 
a, or is its logical contradictory. And knowledge of this kind 
comes, as already said, only from experience of the par- 
ticular facts. The strictly logical contradictory of a is always 
not-a; of wise, not-wise; of cold, not-cold; etc. Mistakes 
frequently arise in stating contradictories in a positive form. 
The difficulty is that terms are chosen which are not true 
logical contradictories. Thus, if we say that every man is 
either wise or foolish, our terms are not contradictories, for a 
middle ground between them is possible. The same would be 
true of divisions like ' large or small,' ' rich or poor,' ^ saint or 
sinner,' 'idle or diligent.' In general, it is safe to scrutinize 
all dichotomic divisions very sharply, to see that the alterna- 
tives are really contradictories. 

The method of dichotomy depends, as we have seen, upon 
the law of Excluded Middle. But there is also another pro- 
cess called Division in logic, which is perhaps better known by 
its less technical name of Classification. In classification, 
there is no necessary limit to the number of classes or divisions 
which may be obtained. In this respect, it, of course, differs 
fundamentally from the twofold division which we have been 
examining. Furthermore, a classification is always made accord- 
ing to some principle which is retained throughout the whole 
process. Any common character istic of thje,.graufix£iadijdd- 
uals to be divided may be taken as a principle of classification. 



8o Definition and Division 

If, however, the characteristic chosen is merely an external 
and accidental one, the classification based upon it will be 
regarded as artificial, and made for some special or temporary 
purposes. Thus we might divide all flowering plants accord- 
ing to the colour of the flowers, or the persons in any company 
according to the pattern of their shoes. A classification which 
proceeds upon such surface distinctions has, of course, no real 
or scientific value, except as it aids us to discover more fun- 
damental or deep-lying resemblances between the individuals 
with which it deals, of which we may regard these superficial 
qualities as signs. Such a preliminary classification corre- 
sponds to what we have called the ^ diagnostic ' definition 

(§ i8). 

A scientific or natural classification, on the other hand, has 
for its purpose the statement of real likeness or resemblance. 
It seeks to find and group together the things which are related 
in some essential point. Consequently, it selects as its princi- 
ple of division some property which appears to be a real mark 
of individuality, and to be connected with changes in other 
properties. Such a real principle of natural classification is 
rarely found by comparison of merely one property or set of 
properties in the things to be compared. To classify accord- 
ing to a single property may be a convenient method of giving 
names to any group of individuals, and of arranging them in 
such a way as to be useful to the student. It does not, how- 
ever, give any adequate idea of the properties and true rela- 
tions of the individuals compared. A really scientific, or 
natural, classification must be based upon a study and com- 
parison of all the discoverable properties of the different in- 
dividuals to be classified. It is only in this way that their 
real resemblance and affinities can be brought to light. 



§ 1 9- Division 8i 

The classification of plants proposed by the famous Swedish bot- 
anist, Karl Linnaeus (1707-1778), was based upon the comparison of 
a single feature : the structure of the sexual organs of plants. This 
method proved of the greatest convenience in indexing plants in a 
convenient way into genera and species so that they could be named 
and described. Yet since the classification adopted was based upon 
a single property or feature of the plant, it was considered (even by 
Linnaeus himself) as merely artificial. Of course it is not so obvi- 
ously artificial as the examples of what we may perhaps call merely 
accidental or trivial classification given above. But Linnaeus's 
system did not aim at setting forth the true relations of plants, and it 
was not based upon any systematic study of all their properties. It 
is useful merely as a stepping-stone to the real study of plants which 
is presupposed in natural classification. 

Certain rules for division are usually given in connection 
with the treatment of this subject. It is not, of course, 
supposed that by their help one can properly divide any 
subject without special knowledge. The purpose of these 
rules is rather to warn against the logical errors to which 
one is most liable in the process of division. 

(i) Every division is made on the ground of difTerences 
appearing in the fundamental nature which is common to 
all the members of the whole to be divided. 

(2) Every division must be based on a single principle 
or ground {fundamentum divisionis), 

(3) The constituent species (or groups into which the 
whole is divided) must not overlap, but must be mutually 
exclusive. 

(4) The division must be exhaustive, ix. the constituent 
species must be equal, when added together, to the genus. 

The first rule requires no remark. It simply states that 



82 Dejinition and Division 

it is only possible to divide any whole on the basis of differ- 
ences in something which is common to all its parts. The 
second rule warns against changing the principle of division 
while the process is being carried out. This law would be 
violated, if, for example, one were to divide mankind into 
Caucasians, Negroes, Mongolians, Europeans, Australians, 
and Americans. The principle of division which was first 
adopted in this example was obviously that of the colour of 
the skin. But this principle was not carried through, and 
another principle, that of geographical distribution, was 
substituted for it. In dividing one must be clearly conscious 
of the principle which one is using, and keep a firm hold of 
it until the division is completed. The example which we 
have just given also violates the third rule. For not all of 
the groups, European, Caucasian, etc., exclude one another. 
Similarly, it would not be good logic to divide animals 
into vertebrates, mammals, insects, birds, mollusks, and fishes. 
The fourth rule simply insists that the division must be 
complete. The whole must be completely included in its 
divisions. It would not be a complete division to say that 
books may be divided into folios, quartos, and duodecimos, 
or vertebrates into mammals and birds. For in neither 
of these examples are the divisions enumerated equal to the 
whole class. 

We have discussed Division as though it always proceeded from 
the whole to its parts, from the genus to its species. But the con- 
trary procedure is quite as frequent, and in the natural sciences is 
the method more usually followed. In this we start with a more or 
less miscellaneous assemblage of objects, examine and compare 
them, and gradually arrange them into groups on the basis of the 
observed likenesses and differences. These groups may again be 



§ 1 9- Division 83 

assembled into more inclusive groups in the same way, and the 
process continued until we have a systematic classification of 
the collection with which we began. The name of Classification is 
often reserved for this procedure, Division being applied only to 
the method already described. As a matter of fact, however, this 
distinction seems to be merely relative. Even classification in this 
narrower sense presupposes some vague idea of the whole, which 
enables us to mark off in a preliminary way the objects to be 
classified from other objects; otherwise its task would be infinite. 
And it is perhaps more usual than not that we classify in both 
ways at the same time. To borrow an illustration from Mr. 
Joseph, ^if one were asked to divide the genus ^^ novel," he might 
suggest a division into the novel of adventure, of character, and of 
plot; but he would at the same time run over in thought the 
novels he had read, and ask himself if they could be classed satis- 
factorily under these three heads.' Division, in fact, in any of its 
forms, presupposes and involves definition. Now definition, as 
we have^feady seen, is based on induction, or an examination 
of the particular things to be defined ; and whether we first notice 
their general likeness one to another, or the special differences 
that exist between them along with this likeness, is largely a 
matter of accident, or is determined by the special purpose of 
the investigation. 

• REFERENCES 

J. S. Mill, Logic, Bk. I., Chs. VII. and VIII. 

W. Minto, Logic Inductive and Deductive, Pt. II., pp. 827130. 

C. Sigwart, Logic, Vol. I., §§ 42-44. 

J. H. Hyslop, The Elements of Logic, Ch. VI. 

H. Rickert, Zur Lehre von der Definition. 



CHAPTER VI 

PROPOSITIONS 

§ 20. The Nature of a Proposition. — A proposition is 
the expression in words of an act of judgment. It is com- 
posed, as we have already seen, of two terms, a subject 
and a predicate, connected by a copula. From the point 
of view of formal logic the predicate is affirmed (or denied) 
of the subject. When we come to consider the nature of 
judgment (cf. especially §§ 78, 81), we shall find reasons 
for questioning whether this analysis of the proposition can 
be regarded as furnishing a correct account of what actually 
takes place in judgment. When we judge, we do not begin 
with' words or terms which are not yet judgments, and then 
pass on to judgment by joining the former together in an 
external way. The conclusions which we shall have*to adopt 
are, that terms represent ways of judging, that the simplest 
act of thought is already a judgment, and that thinking 
develops by advancing from incomplete to more complete 
and comprehensive judgments. The theory of the syllo- 
gism is, however, worked out on the view that the proposi- 
tion expresses a relation between subject and predicate. 
This is sufficiently accurate for practical purposes, and is 
not likely to lead to any serious mistakes so long as we 
remember that it is the proposition, rather than the actual 
nature of judgment, with which we are dealing. 

The logical proposition, as the expression of an act of 

84 



§ 20. Tlie Nature of a Proposition 85 

thought, corresponds to the grammatical sentence. Not 
every sentence, however, is a logical proposition. Sen- 
tences which express a wish or an interrogation do not 
directly enter into the process of argument at all, and may 
therefore be neglected for the present. The same is true 
of exclamatory sentences. Again, even indicative sen- 
tences frequently require to be rewritten in order to reduce 
them to the form of a logical proposition, which demands 
two terms and a copula. The sentence, ^ the sun shines,' 
must, therefore, for purposes of logical treatment, be reduced 
to, ^ the sun is a body which shines.' ^On the hillside 
deep lies the snow,' is expressed as a logical proposition 
in some such form as this: ^The snow is -a covering lying 
deep on the hillside.' It is very important to change the 
grammatical sentence to the regular form of a proposition 
before attempting to treat it logically. 

The most general division of propositions is that which 
classifies them as Categorical and Conditional. A categorical 
proposition asserts directly, and without any condition^ 
The predicate is either affirmed or denied unconditionally 
of the subject. ' Ais B,' ' this room is not cold,' ^ New York 
is the largest city in America,' are examples of categorical 
propositions. Conditional propositions, on the other hand, 
state the consequences which necessarily follow from a 
supposition, or hypothesis, and do not directly assert any- 
thing about particular matters of fact; as, e,g,^ ^ we shall go 
to-morrow, if it does not rain.' ^ It will either rain or snow 
to-morrow,' is also a conditional proposition; for neither 
rain nor snow are asserted directly and absolutely, but in 
each case the appearance of the one is dependent upon the 
non-appearance of the other. 



86 Propositions 

The first of these conditional propositions is known as 
a Hypothetical^ and the latter as a Disjunctive proposition; 
but for the present we shall deal only with categorical propo- 
sitions, and with the form of syllogistic argument to which 
they give rise. After we have completed the account of the 
categorical syllogism, however, it will be necessary to return 
to a consideration of conditional propositions, and to the 
class of arguments in which they are employed. 

§ 21. The Quality and Quantity of Propositions. — We 
shall now consider the various kinds of categorical proposi- 
tions. Such propositions are classified with regard to 
Quality and Quantity. From the standpoint of quality, 
propositions are either Affirmative or Negative. An affirma- 
tive proposition is one in which an agreement is affirmed 
between the subject and predicate, or in which the predicate 
is asserted of the subject. The proposition, ' snow is white,' 
for exanipTe, indicates such an agreement between the sub- 
ject and predicate, and is therefore affirmative in quality. 
A negative proposition indicates a lack of agreement or har- 
mony between the subject and predicate. The predicate does 
not belong to the subject, but all relation or connection be- 
tween the two is denied. 'The room is not cold,' ' the trees 
are not yet in full leaf,' are examples of negative propositions. 

The Quantity of a proposition is determined by the exten- 
sion of the subject. When the proposition refers to all of 
the individuals denoted by the subject, it is said to be Uni- 
versal in quantity. When, on the other hand, the propo- 
sition affirms that the predicate belongs only to a part of the 
subject, it is said to be Particular. For example, ' all metals 
are elements' is a universal proposition, because the assertion 
is made of the subject in its widest or fullest extent; 'some 



§ 21. The Quality and Quantity of Propositions 87 

metals are white ' is a particular proposition, because refer- 
ence is made to only a part of the subject ^ metal.' 

We divide propositions, then, with regard to quantity, 
into Universal and Particular propositions. Universal propo- 
sitions are often indicated by adjectives like ^all,' ^the whole,' 
^every,' etc. It frequently happens, however, that no such 
mark of universality is present. A scientific law is usually 
stated without any explicit statement of its quantity, though 
from its very nature it is meant to be universal. Thus we 
say, ^ the planets revolve around the sun,' ^comets are subject 
to the law of gravitation.' Propositions which have a singu- 
lar or an individual name as subject are often called Indi- 
vidual propositions, as, e.g.^ ^the earth is a planet,' ^know- 
ledge is power.' But since it is impossible to limit a singular 
subject, individual propositions are to be regarded as univer- 
sal. They belong, that is, to the class of propositions which 
employ the subject term in its complete extent. 

Another class, called Indefinite or Indesignate propo- 
sitions, has sometimes been proposed. This class is usually 
said to include propositions in which the form of the words 
does not give any indication whether the predicate is used 
of the whole, or only of a f5fert of the subject. ^Men are to 
be trusted/ ^animals are capable of self-movement,' may 
serve as examples. This classification may be useful in 
illustrating the evil of making indefinite or ambiguous 
statements. Otherwise there is nothing to be learned from 
it. A really indefinite propositioi^ has no place in an argu- 
merXinrng wiric rightfully refus^ to deal with it. The first 

If a subject is-: is that our statements shall be clear and 
latter must not osition is not necessarily indefinite, how- 
proposition. Takes no qualifying words like 'all' or 'some.' 

\ 



88 Propositions 

It is the meaning of a proposition as a whole, rather than the 
form of its subject, which renders it definite or indefinite* 
Where, on the other hand, it is really impossible to decide 
whether the proposition is universal or particular, logic 
forbids us to proceed with the argument until this point 
has been made clear. 

Particular propositions are usually preceded by some 
word or phrase which shows that the subject is limited 
in the extent of its application. The logical sign of particu- 
lar propositions is ^some,' but other qualifying words and 
phrases, such as 'the greatest part,' 'nearly all,' 'several,' 
'a small number,' etc., also indicate particularity. Here 
again, however, it is the meaning of the proposition, rather 
than its form, which is to be considered. 'All metals are 
not white,' for example, is a particular proposition, although 
introduced by 'all,' since it is clearly equivalent to 'some 
metals are not white.' 'Every mark of weakness is not a 
disgrace,' again, is a particular proposition, and signifies 
that 'not all, or some marks of weakness are not disgraceful.' 

The words 'few' and 'a few' require special attention. 

The latter, as in the proposition, ' a few persons have spoken 

to me about it,' is equivalent to 'some,' and introduces a 

particular affirmative proposition. 'Few,' on . the other 

hand, is negativain character. Thus, 'few were saved from 

the shipwreck' implies that only a few were saved, or that 

the greater number did not escape, and the proposition is 

therefore to be considered as a particular negative. 

Propositions, then, are classified as affirmat^* " „ ' ^^ga- 
. ^ , . . , , . 1 . ^ pie? 2.11 metais 

tive m Quality, universal and particular m C _ 
- , .^ . 1.1 ise the assertion 

these classifications are combined, we e 

st extent * some 
propositions, to symbolize which the vov 



§ 22. Difficulties in Classification 89 

employed. A and I, the vowels contained in affi^rmo^ stand for 
affirmative propositions; E and O, the vowels in nego, for neg- 
ative propositions. This may be represented as follows : — 

, f Affirmative: All S is P.^j^^^'^'^ A' 

Universal \ ^^ . ^. ^ . ^ ^ 

[Negative: No S is P. E 

^ . , f Affirmative : Some S is P. I 

Particular \ ^^ . ^ ^ . ^ ^ 

\ L Negative : Some S is not P. O / 

We shall henceforth use A, E, I, and O to represent respec- 
tively a universal affirmative, a universal negative, a particu- 
lar affirmative, and a particular negative proposition. In 
dealing with propositions logically, the first step is to reduce 
them to one or other of these four types. This can be 
accomplished readily by noticing the distinctions previously 
laid down. There are, however, certain grammatical 
forms and sentences which present some difficulty, and it 
may therefore be useful to consider them separately. 

§22. Difficulties in Classification. — In the first place, 
we may notice that in ordinary language the terms of a 
proposition are frequently inverted, or its parts separated 
in such a way that it requires attention to determine its true 
logical order. In the proposition, ^now came still evening 
on,' for example, the subject ^ still evening' stands between 
two portions of the predicate. As a logical proposition, the 
sentence would have to be expressed in some such form as 
the following: ' Still evening is the time which now came on.' 
Similarly, we should have to write an inverted sentence 
like, ^deep lies the snow on the mountain,' as ^the snow is 
something which lies deep on the mountain.' 

If a subject is qualified by a relative clause, the verb of the 
latter must not be confused with the main assertion of the 
proposition. Take the sentence, 'he is brave who conquers his 




go Propositions 

passions.' Here it is evident that the relative clause describes 
or qualifies ^ he. ' Logically, then, the proposition is of the form 
A, and is to be written, ^ he who conquers his passions is brave.' 
The reader will notice that all propositions which begin with 
pronouns like ' he who,' ' whoever,' etc., are universal in quan- 
tity, since they mean all who belong to the class in question. 

(i) We have reduced grammatical sentences to logical propo- 
sitions by changing the form in such a way as to have two terms 
united by ^ is ' or ^ are ' as the copula. Such a proposition, however, 
does not express time, but simply the relation existing between 
subject and predicate. When the grammatical sentence does 
involve a reference to time, and especially to past or future time, 
the reduction to logical form is somewhat awkward. Perhaps the 
best method is to throw the verb expressing time into the predi- 
cate. Thus *the steamer will sail to-morrow' = ^the steamer is a 
vessel which will sail to-morrow ' ; ^ we waited for you two hours yes- 
terday ' = ^ we are persons who waited for you two hours yesterday. ' 

(2) Exclusive propositions exclude all individuals or classes 
except those mentioned by the use of some such word as ^except,' 
'none but,' 'only.' 'None but the guilty fear the judge'; 'only 
citizens can hold property'; 'no admittance except on business.' 
These propositions may all be reduced to the form E by writing 
'no' before the contradictory of the subject term. Thus 'none but 
the guilty fear the judge' = 'no one who is not guilty fears the 
judge'; 'only citizens can hold property' = 'no one who is not a 
citizen, etc.'; 'no admittance except on business' = 'no person 
who has not business is to be admitted.' Or, by taking the predi- 
cate as subject, the meaning of the proposition may be expressed 
H\^^ffirmatively : ' all who fear the judge are guilty ' ; 'all who can 
old property are citizens.' 

§23. Formal Relation of Subject and Predicate. — We 

have now to consider how the relation existing between 



-4 



§ 23- Formal Relation of Subject and Predicate 91 

the terms of a proposition is to be understood. In § 16 it was 
shown that every term may be interpreted in two ways : either 
from the point of view of extension, or from that of intension. 
Extensively, terms are taken to represent objects or classes of 
objects; while their meaning in intension has reference to the 
attributes or qualities of things. Now the interpretation of the 
categorical proposition given by formal logic is based entirely 
on extension. That is, the subject and predicate are regarded 
as standing for individual objects or classes of objects. The 
question to be considered, then, concerns the extensive relation 
of these groups of objects in the propositions A, E, I, andO. 
This mode of interpreting propositions must not be taken 
as furnishing an adequate theory of the nature of the act of 
judgment which is expressed in the proposition. It leaves 
entirely out of account the intensive meaning, or the con- 
nection of attributes asserted by the proposition, which 
in many cases is the most prominent part of its signification. 
Thus the proposition, ' all metals are elements,' implies that 
the quality of being an element is united with the other 
qualities connoted by the term ^ metal.' Indeed, this inter- 
pretation is perhaps more natural than the one given by 
formal logic, namely, that the class of metals is included in 
the class of elements. It must be admitted that the extensive 
way of reading propositions, as affirming or denying the 
inclusion of one class of objects in another class, frequently 
seems artificial. Nevertheless, it is the view upon which 
the historical account of the syllogism is founded. And the 
fact that this mode of representing the meaning of proposi- 
tions leads in practice to correct conclusions proves that it is 
not wholly false. It represents, as we have seen in discussing 
terms (§ 16), one side or aspect of the meaning of propositions. 



92 Propositions 

From the point of view of formal logic, then, a logical 
proposition signifies that a certain relation exists between 
the class of things denoted by the subject, and that denoted 
by the predicate. This relation may be one of inclusion or 
of exclusion. For example, the proposition ' all good men 
are charitable,' is interpreted to mean that ' good men' are 
included in the class of ' charitable men.' On the other 
hand, ^no birds are mammals,' signifies that the two classes, 
* birds ' and ^ mammals,' are mutually exclusive. The mean- 




FlG. I. 

ings of the four logical propositions A, E, I, and O may be 
represented by means of a series of diagrams, which were 
first used by the celebrated German mathematician Euler, 
who lived in the eighteenth century. 

To represent the meaning of a proposition in A, like ' all good 
men are charitable,' we draw a circle to symbolize the class of 
charitable beings, and then place inside it a smaller circle to 
stand for good men. The proposition, that is, signifies that 
^good men' are included in the class of ^charitable beings.' 
The subject belongs to, or falls within, the larger class of 
objects represented by the predicate. 

It must be carefully noted that proposition A does not usu- 
ally assert anything of the whole of its predicate. In the ex- 



§ 23- Formal Relation of Subject and Predicate 93 

ample just given, no assertion is made regarding the whole 
class of ' charitable beings/ but only in so far as they are 
identical with ^good men.' There may possibly be other 
charitable beings who are not good men, or not men at all. 
The meaning of the proposition, then, is that ' all good men 
are some charitable beings.' In other words, the predicate 
of the ordinary universal affirmative proposition is taken 
only in a partial, or limited extent: nothing is affirmed of 
the whole of the circle of charitable beings. We denote 
this fact by saying that the predicate of proposition A is 
undistributed. The subject, on the other hand, as a universal 
term, is employed in its fullest extent, or is distributed. 

In some cases, however, the predicate is not a broader 
term which includes the subject, but the two are equal in 
extent. In the proposition, ^ all equilateral triangles are 
equiangular,' for example, this is the case. If we were 
to represent this proposition graphically, the circle of equi- 
lateral triangles would not fall inside that of equiangular 
triangles, but would coincide with it. The same relation 
between subject and predicate holds in the case of log- 
ical definitions. For example, in the definition, -mon- 
archy is a form of political government where one man 
is sovereign,' the subject is coextensive with the whole 
of the predicate. In examples of this kind, it is of course 
obvious that the predicate, as well as the subject, is distributed. 

As an example of proposition E, we may take the example, 
' no birds are mammals.' The meaning of this proposition is 
represented graphically by means of tw^o circles falling out- 
side each other as in Fig. 2. 

The proposition asserts that the class of birds falls com- 
pletely without the class of mammals, that the two classes 



94 Propositions 

are entirely distinct, and mutually exclusive. With regard 
to quantity, the subject is of course universal or distributed' 
And, in this case, the predicate is also distributed. For the 
proposition asserts that the subject ' birds ' does not agree with 
any part of ' mammals.' Or, in terms of the diagram, we deny 
that the circle representing ' birds ' corresponds with any 




Fig. 2. 



portion of the circle ' mammals.' But to exclude the former 
circle completely from the circle which represents ' mammals,' 
it is necessary that we know the whole extent of the latter. 
Otherwise we could not be sure that the subject had not some 
point in common with it. Proposition E, therefore, distributes, 
or uses in their widest extent, both subject and predicate. 

The meaning of a proposition in I, as, e,g., ' some birds are 
web-footed,' is shown by means of two circles intersecting or 
overlapping as in Fig. 3. A part of the class of birds corre- 
sponds with a part of web-footed animals. The proposition 
has reference to the common segment of the two circles, which 
may be large or small. The two circles correspond in part at 
least. In proposition I, both subject and predicate are undis- 
tributed. The subject is, of course, a particular or limited 
term. And, as will be clear from what has already been said 
in the case of proposition A, reference is made only to a 
limited portion of the predicate. In the example used, the 



§ 23- Formal Relation of Subject and Predicate 95 

assertion refers only to those web-footed animals which are 
also birds. Or we may say that the proposition has reference 
only to the common segment of the circles representing sub- 




FiG. 3. 

ject and predicate. Nothing is asserted of the other portions 
of the two circles. In other words, both subject and predicate 
are employed in a limited extent, or are undistributed, 

' Some metals are not white,' may serve as an example of 
proposition O. 

This proposition may be represented graphically as in 
Fig. 4. Though this is the same form of diagram as that 




Fig. 4. 



employed in the last figure, the proposition refers now to the 
outlying part of the circle 'metal.' Some metals, it asserts. 



q5 Propositions 

do not fall within the sphere of white substances. A larger or 

smaller section of the circle representing the former term, falls 

completely without the circle of white substances. 

It is necessary to notice carefully that although the subject 

of O is undistributed, its predicate is distributed. For, as we 

have seen, a part of the subject is completely excluded from 

J the class of ^ white substances.' But in order to exclude from 

Of l^^^r); part of the predicate, the full extent of the predicate must 

I fbe known. Or, in terms of the diagram, the proposition ex- 

^ 1^ {eludes a portion of the circle of metals (some metals) from 

f^ j each and every part of the circle of white things. The latter 

V I term must therefore be used in its full extent, or be distributed. 

\ It is absolutely necessary, in order to comprehend what 

C^ f follows, to understand the distribution of terms in various 

< I propositions. It may help the reader to remember this if 

1 ^ we summarize our results in the following way: — 
O ^^^^.^^ 

Proposition A, subject distributed, predicate undistributed. 
Proposition E, subject distributed, predicate distributed. 
Proposition I, subject undistributed, predicate undistributed. | 
Proposition O, subject undistributed, predicate distributed. J 

REFERENCES TO §23 

J. N. Keynes, Studies and, Exercises in Formal Logic, Part II., Chs. I. 
and II. 

J. S. Mill, Logic, Bk. I., Ch. V. 

C. Sigwart, Logic, §5. 

B. Bosanquet, The Essentials of Logic, Lectures V. and VI. 




CHAPTER VII 

THE INTERPRETATION OF PROPOSITIONS 

§ 24. The So-called Process of Immediate Inference. — 

Many logicians speak of two kinds, or processes of reasoning, 
to which they give the names of Mediate, and Immedjate 
inference. Mediate inference, it is said, asserts the agree- 
ment or disagreement of a subject and predicate after hav- 
ing compared each with some common element or middle 
term. The conclusion is thus reached mediately or indirectly. 
The syllogism is the best example of mediate inference. In 

the syllogism, 

All M is P, 

All S is M, 

Therefore S is P, 

the conclusion is reached through the medium of M, with 
which both S and P have been compared. It will be noticed 
that to obtain a conclusion in this way two propositions or 
premises are necessary. 

We sometimes are able, however, to pass directly or imme- 
diately from one proposition to another. For example, the 
proposition that ' no men are infallible,' warrants the statement 
that ' no infallible beings are men.' Or, if we know that it is 
true that 'some birds are web-footed,' we perceive at once that 
the proposition, ' no birds are web-footed,' is false. It is this 
H 97 



g^6 The Interpretation of Propositions 

process of passing directly from one proposition to another 
which has been named by many logicians Immediate infer- 
ence. 

The question may be raised, however, whether the direct 
passage from one proposition to another, as in the above 
examples, should properly be called inference, or whether 
the change is not merely in the verbal expression. As we 
have already shown, inference is a process of exhibiting the 
relation of facts to one another by discovering some common 
element or connecting principle by means of which they are 
united (cf. also § 92). Wherever we can discover a connect- 
ing thread or common element between two facts or 
groups of facts, we are able to infer with greater or less 
certainty from the nature of the one what the nature of 
the other must be. But it is essential to inference that 
there shall be a real transition from one fact to another — 
that the conclusion reached shall be different from the 
starting-point. 

The point at issue, therefore, is whether a new fact or truth 
is reached in the so-called processes of immediate inferences, 
or whether we have the same fact repeated in the form of a new 
proposition. When we pass from ' no men are infallible,' to 
^no infallible beings are men,' can we be said to infer a new 
truth ? In this case it is evident, I think, that there has been no 
real development or extension of the original proposition so as 
to include a new fact. The new proposition is the result of a 
verbal interpretation of the original one, and restates the same 
fact in a different way. Inference always completes or enlarges 
the truth from which it sets out by showing the reasons which 
support it, or the consequences which follow from it. Now, 
when we pass directly from one proposition to another, as 



§ 25- The Opposition of Propositions 99 

in the examples given above, it will be found, I believe, 
that nothing new has been added to the original state- 
ment — no new facts have been brought into connection 
in the process. 

Nevertheless, the process does not appear to be merely 
verbal, but to involve a certain movement of mind, — a fuller 
and clearer realization of the meaning and bearings of the 
original proposition. Before deciding the matter, the claims 
of each of the different types of so-called immediate inference 
should be examined separately; and the question is one that 
the student should keep in mind throughout the chapter. 
Some authors have named these processes ' Eduction,' since 
they draw out or explicate the meaning of propositions. 
Whether or not they may properly be called inference^ they 
render important service in helping us to understand all 
that is really implied, both in the way of affirmation and 
denial, in the propositions we use. Nothing is commoner in 
argument than disputes as to what certain statements imply — 
what propositions ^ amount to the same thing,' and may there- 
fore properly be substituted for any given statement. Now it 
is the purpose of the methods of logical interpretation (or im- 
mediate inference) which are to be discussed in this chapter, to 
determine what other statements, positive or negative, are 
really involved in the case of the different forms of logical propo- 
sition. Given a certain proposition as true or false, what other 
propositions can be immediately derived from it ? We may 
consider under the following five headings the results obtain- 
able by processes of Immediate Inference, or direct Interpreta- 
tion: Opposition^. Obversion, Conversion, Contraposition, 
Jnyersion. 

§ 25. The Opposition of Propositions. — We have seen that 



100 The Interpretation of Propositions 

all categorical propositions have to be reduced to one of the 
four forms, A, E, I, O, in order to be dealt with by logic. Now, 
between these propositions, all of which have the same subject 
and predicate, certain relations of exclusion and inclusion exist, 
to which the general name of Opposition has been given. It is 
clear that the truth of some of these propositions excludes the 
truth of others, and also that the relation between certain of 
the propositions is such that one assertion necessarily involves 
the truth of another. Logical Opposition, then, isjise4^to 
.denote any relation, either of exclusion or inclusion, that exists 
between propositions having the same subject and predicate^,^^ 
Thus, if it be true that ^ no professional gamblers are honest,' 
it is impossible that ' all professional gamblers are honest,' or 
even that some are honest. The proposition E is thus incon- 
sistent with both A and I. Again, if it be true that ^ all politi- 
cians are dishonest,' it must be true that ' some politicians are 
dishonest,' as well as false that ^no pohticians are dishonest.' 
That is, when A is true, I is also true, while E is necessarily 
false. Propositions A and E are called Contrary propositions. 
' All A is B,' and ' no A is B,' express the greatest possible de- 
gree of contrariety or opposition. If one proposition be true, 
the other is necessarily false. It is to be noticed, however, 
that we cannot conclude that if one be false, the other is true. 
For both A and E may be false. Thus, for example, the 
propositions, 'all men are wise ' and ^no men are wise,' are 
both false. But, on the other hand, propositions A and O, 
E and I, are pairs of Contradictory propositions : if one is false, 
its contradictory is necessarily true; and if one is true, the 
other is manifestly false. 

The relation of the four logical propositions is clearly 
shown by arranging them in the following way: — 



§ 25. The Opposition of Propositions 

^ Contraries £ 



lOI 




/ 



Sub-Contraries 
Fig. 5. 



A and E are known as contraries; I and O as suhcontraries; 
A and O, I and E, as contradictories; A and I, E and O, as 
subalterns. 

The relations of these propositions may now be summed up 
in the following statements: — 

(i) Of contrary propositions, one is false if the other is true, 
but both may be false. 

(2) Of contradictory propositions, one is true and the 
other necessarily false. 

(3) If a universal proposition is true, the particular which 
stands under it is also true; but if the universal is false, the 
particular may or may not be true. 

(4) If a particular proposition is true, the corresponding 
universal may or may not be true; but if the particular is false, 
the universal must be false. 



\ 



\ 



\ 



I02 The Interpretation of Propositions 

(5) Subcontrary propositions may both be true ; but if one 
is false, the other is necessarily true. 

The knowledge that any one of these propositions is either 
true or false enables us to determine the truth or falsity of at 
least some of the others. 

For example, if A is true, E is false, O is false, and I is true. 
If A is false, E is doubtful, O is true, and I doubtful. 

If I is true, E is false, A is doubtful, and O doubtful. If I is 
false, E is true, A is false, and O true. 

Similarly, we are also able to determine what follows when 
we suppose that E and O are either false or true. 

It ought to be carefully noted that when we affirm the truth of 
the particular proposition I, we do not deny the truth of the universal 
proposition A. The proposition, ^ some students are fond of recrea- 
tion,' for example, does not exclude the truth of ^ all students are 
fond of recreation.' Similarly, the truth of O does not exclude the 
corresponding proposition in E : the statement, ^ some men are not 
generous,' for example, does not interfere with the truth of the uni- 
versal proposition, ^ no men are generous. ' A particular proposition , 
in other words, asserts something of a limited part of a subject; 
it neither affirms nor denies anything of the same term taken 
universally. 

The reader will remember that propositions which have 
the name of some singular or individual thing as subject, have 
been classified as universal. ' New York is the largest city in 
America,' ^charity is not the only virtue,' are examples of such 
propositions. Now it is at once evident that in cases of this 
kind there are no corresponding particular propositions. 
What has just been said regarding the relation of universal 
and particular propositions, applies therefore only to propo- 
sitions which have a general term or name as subject. 



§ 26. The Obversion of Propositions 103 

Moreover, we must notice that when A and E proposi- 
tions have a singular or individual name as subject, the 
relations between them are somewhat different from those 
just stated. A and E, we said, are contrary, but not contradic- 
tory propositions. By that it was implied that although we 
can proceed from the truth of the one to the falsity of the other, 
it is not possible to go in a converse direction, from falsity to 
truth. We cannot conclude, for example, from the falsity of 
the proposition that ' all men are selfish ' the truth of the corre- 
sponding negative proposition, ' no men are selfish.' With 
contradictory propositions, however, we can go from a 
denial to an affirmation. Now the point to be observed, with 
regard to propositions with a singular term as subject, is that 
although only contraries in form, they have yet the force of 
contradictories. ' Socrates is wise ' (A) , and ^ Socrates is not 
wise' (E), are contradictory, as well as contrary, propositions. 
§ 26. The Obversion of Propositions. — The terms ^ Ob- 
version ' and ^ iEquipollence ' were formerly used to denote 
any process by which the form of a proposition is changed 
without an alteration in meaning being involved. The 
name ^Obversion' is, however, now generally employed to 
describ£^e change undergoes in passin^_ 

from the affirmative to the negative, or from the negativ.e„l£U^ 
"the affirmative form while still retaining its original meaning^.^^ 
"^"Every fact is capable of expression either in the form 
of an affirmative or of a negative proposition. Whether 
the affirmative or negative form is chosen in any particular 
case, is partly a matter of convenience. It is also deter- 
mined largely by the psychological interest of the moment, 
ix, by the purpose which we have in view in making the 
assertion. When, for example, we wish to repel some sug- 



104 T^^ Interpretation of Propositions 

gestion which may have occurred to us, or to deny something 
which our companions appear to beheve, we naturally choose 
the negative form of statement. But the meaning of the 
proposition is the same whether we say, ^ all men are falli- 
ble,' or, ^no men are infallible.' Similarly, we can say, ^not 
one of the crew escaped,' or, ^ all of the crew perished.' 

Ob version, then, is the process of substituting for any 
affirmative proposition its equivalent in negative form, 
or of expressing the meaning of a negative proposition as an 
affirmative. To obtain the obverse of proposition A, we 
proceed on the principle that two negatives are equal to an^ 
affirmative. Instead of ^ all animals digest food,' we may 
write, ^(figvanimalsl are beings that do not digest food'; for, 
' every man has his own troubles,' ^ there are no men who 
have not their own troubles.' Instead of affirming the 
predicate of the subject, the obverse of A takes the contra- 
dictory of the original predicate and denies it universally. 

Proposition I may be ob verted in the same way, though 
it yields a particular, instead of a universal negative propo- 
sition. Thus the obverse of, ' some of the houses are com- 
fortable,' is ' some of the houses are not not-comfortable,' 
i.e, uncomfortable. We deny the negative predicate in the 
obverse proposition, instead of affirming the positive. 

We obtain the obverse of the propositions E and O by 
changing the negation contained in them to its equivalent 
affirmation. This is done by attaching the negative to the 
predicate, and then affirming it of the subject. For example, 
to obtain the obverse of, ^ no one who was present can forget 
the scene,' we first write the proposition in logical form, 
' no one who was present is a person who can forget the scene.' 
Now the contradictory of the predicate term, ' a person who 



§ 2/. The Conversion of Propositions 105 

can forget the scene/ is, ^ a person who can not forget the 
scene.' Affirming this universally we get, ' all persons who 
were present are persons who cannot forget the scene.' As 
an example of how the obverse of O is obtained, we may 
take the proposition, ^ some metals are not white.' Now if 
we change the quality of the proposition by attaching the 
negative to the predicate, we obtain, ^ some metals are not- 
white.' That is, instead of denying, we affirm the contra- 
dictory of the original predicate. When the predicate is made 
up of several words, it is important that the logical contra- 
dictory of the whole term be taken. For example, in the 
proposition, ^ some men are not fond of work,' the predicate 
fully expressed is, ' persons who are fond of work.' Now 
the negative or contradictory term corresponding to this is, 
^ persons who are not fond of work.' The obverse of the 
original proposition therefore is, ^ some men are persons 
who are not fond of work.' 

§ 27. The Conversion of Propositions. — To convert_a_ 
pro2^ositionjs_Jto__ tonspose i t s sub j ec t and predicate -so- 4ba^ 
each shalLo€eupy-4he place previously held by the pthej:^. 
Thus the proposition, ^ no men are infallible,' is converted 
by writing it, ^ no infallible beings are men.' The original 
proposition is called the Coavertend, and the proposition 
obtained by conversion the Conyerse. By conversion, then, 
a proposition having P as its subject is derived directly 
from the original form of the assertion S — P. It is for this 
reason that conversion is usually ranked as a process of 
immediate inference. For it makes clear what is involved 
in the original proposition but is perhaps not clearly rec- 
ognized ; namely, that in the assertion S — P some statement 
about P as subject in its relation to S is also involved. 



io6 The Interpretation of Propositions 

Whether this may more properly be regarded as a process of 
formal interpretation, than as one which involves real infer- 
ence, is a question which the student may consider for himself. 

It is evident that in proceeding to convert propositions 
it will be necessary to notice whether the predicate of the 
convertend, or proposition to be converted, is distributed 
or undistributed, otherwise we should not know what exten- 
sion to apply to this term when used as the subject of the 
converse proposition. The rules usually given to hmit 
the process of conversion are as follows: — 

(i) No term must be distributed in the converae propo- 
sition which was npt3istributed in the convertend. 

(2) The quality of the converse proposition must remain 
the same as the quality of the convertend. 

The reason for the first rule is at once evident from what 
has been already said. The second rule is not one which is 
always observed. Of course, the meaning of a proposition 
must not be altered by changing the quality simply or 
directly. But, in converting by Contraposition, as we shall 
see later, it is first necessary to obtain the equivalent of 
the convertend by obversion, and this necessarily involves 
a change of quality. 

There are two kinds of conversion usually recognized: 
[a) Simple Conversion; (&) Conversion by Limitation or 
per accidens, 

(a) By Simple Conversion is meant the direct transposition 
of the subject and predicate without any other change in 
the form of the proposition. Both propositions E and I 
can be converted in this way. Thus the converse of, ' none of 
the books on this shelf are novels,' is another proposition in 
E, ' no novels are books on this shelf.' From ' some dicoty- 



§27- The Conversions of Propositions 107 

ledons are exogens ' we obtain by conversion another particu- 
lar affirmative proposition, ^ some exogens are dicotyledons/ 

(&) Conversion by Limitation or per accidens is applied 
to proposition A. In this process A loses its universality, 
and yields as a result only proposition I. To illustrate 
lliis mode of Conversion we may take the proposition, ' brown 
hematite is an iron ore? As we already know, the term 
^an iron ore,' being the predicate of proposition A, is undis- 
tributed. When used as the subject of a new proposition, 
therefore, it must be limited by the adjective ' some.' We 
thus obtain the converse proposition, ' some iron ore is 
brown hematite.' Similarly, the converse of the proposition, 
' all sensations are mental processes,' is ^ some mental pro- 
cesses are sensations.' When proposition A is converted by 
limitation, then, it yields proposition I as a result. And it 
is evident that the proposition has really lost something in 
the process. For it is impossible by converting again to 
obtain anything more than a particular proposition. It is, 
however, sometimes possible to convert proposition A with- 
out limiting the predicate. In formal definitions, for example, 
the subject and the predicate are of equal extent, and may be 
transposed simply without any limitation of the latter. Thus 
the converse of, ^ an equilateral triangle is a plane figure 
having three equal sides,' is ' a plane figure having three 
equal sides is an equilateral triangle.' 

Proposition O is the only form of logical proposition that 
does not admit of Conversion. E and I, as we have seen, 
may be converted simply, and the converse of A is obtainable 
by limitation, or even in some cases by simple Conversion. 
But from an O proposition, 'some S is not P,' no proposition 
where P is subject and S predicate can be obtained. And 



io8 The Interpretation of Propositions 

the reason for this may be seen at once. For if the conver- 
sion were made, giving the form 'some P is not S,' S would 
be distributed as the predicate of a negative proposition. 
But in the convertend (' some S is not P ') it was not distrib- 
uted; accordingly, an attempt to convert O involves a breach 
of the rule that no term must be distributed in the converse 
proposition which was not distributed in the convertend. 

§ 28. Contraposition and Inversion. — In Contraposition 
the contradictory of the predicate of the original proposijtion 
is taken as the subject of a new assertion. That is, the Contra- 
positive of a proposition of the form S — P, has as its suFJecr 
non-P, the contradictory of P. Contrapositive propositions 
may be derived from A, E, and O. Proposition I, for reasons 
that will be evident later, does not yield a contrapositive. 

The contrapositive of A, E, and O may be obtained 
through two steps: by first ob verting and then converting. 
After some practice in deriving the contrapositive in this 
way the student should learn to obtain it directly, remem- 
bering that what is required is a statement as to what is 
implied in the original proposition regarding non-P, the 
contradictory of the predicate. Let us first, however, illus- 
trate the longer method. 

If we take as an example of A the proposition ' all the plan- 
ets are bodies that revolve around the sun,' we can obtain 
the contrapositive by (i) ob verting/ no planets are bodies 
that do not revolve around the sun,' and (2) converting the 
E proposition obtained by ob version, 'No bodies that do not 
revolve around the sun are planets.' This is in the form 
' no non-P is S,' and we might therefore write the contra- 
positive of A directly, by taking the contradictory of the 
original predicate and denying it universally of the subject. 



§ 28. Contraposition and Inversion 109 

The form here derived, the converse of the obverse, has 
usually been defined as the contrapositive of a given propo- 
sition, and we have so far followed this definition. But 
some logicians speak of the contrapositive as a proposition 
which has the same quality as the original, and has the more 
symmetrical form ^ non-P — non-S/ This maybe obtained 
by ob verting the result obtained in the last paragraph, 
^ all bodies that do not revolve around the sun are non- 
planets.' The two forms are not essentially different, but 
we may follow what appears to be the best usage by speaking 
of the form ^ non-P — S,' as the partial contrapositive, and 
^ non-P — non-S ' as the full contrapositive. 

Taking as an example of E the proposition ^ none that 
love anghng are wholly given over to the world,' we obtain 
(i) by Ob version, ^ all that love angling are persons not wholly 
given over to the world,' and (2) by Conversion of this latter 
proposition,l/ some persons not wholly given over to the 
world are those who love angling.' This is the partial 
contrapositive, which when ob verted gives us the full contra- 
positive, ^ some persons not wholly given over to the world 
are not those who do not love angling,' a negative proposition 
like the E from which it is derived, and which has the form 
^ some not-P is not not-S.' It is especially to be noted 
that the contrapositive of E is a particular proposition. 

To obtain the contrapositive of O, we proceed in the same 
way, first ob verting, then converting the result for the 
partial contrapositive, and ob verting once more for the 
full contrapositive. For example, ^some things that glitter 
are not gold'; (i) by ob version, ^some things that ghtter 
are not-gold ' (i.e. substances other than gold) ; (2) by con- 
version, ' some substances other than gold are things that 



no The Interpretation of Propositions 

glitter'; (3) by ob version, ^some substances other than gold 
are not things that do not glitter.' 

Inversion. The original proposition has S as subject and 
P as predicate; the converse has P as subject and S as 
predicate ; the contrapositive, non-P as subject, and in its 
full form, non-S as predicate. It is clear that the only remain- 
ing term to be used as a subject is non-S. Now, where an 
assertion is made regarding this — the contradictory of the 
original subject — the form is known as the Inverse. The 
question now is: What logical propositions of the form 
S — P enable us to derive a proposition about what is not-S ? 
By experimenting in applying obversion and conversion we 
find that only the Universal propositions, A and E, yield 
the Inverse form, and also that this is always a particular 
proposition. From ^ All S is P,' we may derive, by alternately 
ob verting and converting, 'some not-S is not-P' (which may 
be called the full Inverse by analogy with the terms em- 
ployed in regard to contraposition), which by obversion 
gives ' some not-S is not-P,' the partial Inverse.^ Similarly, 
from 'no S is P ' may be derived the full Inverse, 'some not-S 
is not not-P,' which yields, by obversion, ' some not-S is P.' 

* Keynes {Formal Logic^ 4th ed., pp. 139-40) calls attention to the apparent 
error in passing from * All S is P,' — where P is not distributed — to, ' Some not 
S is not P/ — where P is distributed. The result seems an error, yet it is 
impossible to discover any mistake in the processes of conversion and obversion 
by which it has been obtained. This difficulty may serve to illustrate the 
impossibility of proceeding logically without assumptions even where the trans- 
formations appear to be purely formal. Keynes says : " It is in the assumption 
of the existence of the contradictory of the original predicate that an explanation 
of the apparent anomaly may be found. That assumption may be expressed 
in the form, 'Some things are not P.* The conclusion 'Some not-S is not P' 
may accordingly be regarded as based on this premise combined with the ex- 
plicit premise, 'AH S is P'; and it will be observed that, in the additional 
premise, P is distributed." 



§28. Contraposition and Inversion 



III 



We have already summarized results with regard to the 
Opposition of propositions (p. loi). For the sake of con- 
venience the outcome of the other processes may be brought 
together in the following table^ given by Keynes.^ S' and P' 
are used to denote not-S and not-P. 








A 


I 


E 


O 


Original proposition 


SaP ' 


SiP 


SeP 


SoP 


ii 


Obverse 


SeP' 


SoF 


SaP' 


SiP 


iii 


Converse 


PiS 


PiS 


PeS 




iv 


Obverted Converse 


PoS' 


PoS' 


PaS' 




V 


Partial Contrapositive 


FeS 




P'iS 


P'iS 


VI 


Full Contrapositive 


P'aS' 




P'oS' 


P'oS' 


vii 


Partial Inverse 


S'oP 




S'iP 




viii 


Full Inverse 


S'iP' 




S'oP' 





REFERENCES 



B. Bosanquet, Logic^ Vol. I., pp. 310-319. 
W. Minto, Logic Inductive and Deductive^ Pt. III., pp. 130-166. 
J. N. Keynes, Studies and Exercises in Formal Logic, 4th ed., Chs. 
III., and IV. 

* Op. cit.y p. 140. 



CHAPTER VIII 

THE SYLLOGISM 

§ 29. The Nature of Syllogistic Reasoning. — The syl- 
logism, as we have already seen (§ 10), presents a conclusion 
together with the reasons by means of which it is supported. 
A single proposition taken by itself is dogmatic: it merely 
asserts, without stating the grounds upon which it rests. 
The syllogism, on the other hand, justifies its conclusion 
by showing the premises from which it has been derived. 
It thus appeals to the reason of all men, and compels their 
assent. To do this, it is of course necessary that the truth of 
the premises to which appeal is made should be granted. 
If the premises are disputed or doubtful, the argument 
is pushed a step further back, and it is first necessary to 
show the grounds upon which these premises rest. The 
assumption of syllogistic reasoning — and, indeed, of all 
reasoning whatsoever — is that it is possible to reach 
propositions which every one will accept. There are certain 
facts, we say, well known and established, and these can 
always be appealed to in support of our conclusions. In 
syllogistic reasoning, then, we exhibit the interdependence of 
propositions; ix,, we show how the truth of some new propo- 
sition, or some proposition not regarded as beyond question, 
follows necessarily from other propositions whose truth 
every one will admit. 

112 



§ 29. The Nature of Syllogistic Reasoning 113 

The question which arises in connection with the syllogism, 
therefore, is this : Under what conditions do propositions which 
are accepted as true contain or imply a new proposition as a 
conclusion ? Or we may put the question in this form : In 
what ways may the four kinds of logical propositions, A, E, I, 
O, be combined so as to yield valid conclusions ? 

We pointed out in a previous chapter that a syllogism has 

always two premises. It is, however, impossible to obtain a 

conclusion by combining any two propositions at random, 

as e.g.,— 

All A is B, 

NoXisY. 

It is evident that any two propositions will not yield a con- 
clusion by being taken together. In order to serve as premises 
for a syllogism, propositions must fulfil certain conditions, and 
stand in certain definite relations to each other. To deter- 
mine some of the most apparent of these conditions, let us 
examine the argument : — 

All mammals are vertebrates, 
The whale is a mammal. 
Therefore the whale is a vertebrate. 

It will be noticed that the term ' mammal ' is common to both 
premises, and that it does not occur at all in the conclusion. 
Moreover, it is because the other terms are compared in turn with 
this common or Middle Term and found to agree with it, that 
they can be united in the conclusion. It is only propositions 
which have a middle term, therefore, v/hich can be employed 
as the premises of a syllogism. The syllogism is thus essen- 
tially a process of comparison. Each of the terms entering into 
the conclusion is compared in turn with the same middle term, 
I 



114. ^^^^ Syllogism 

and in this way their relation to each other is determined. 
We reach the conclusion not directly or immediately, but 
by means of the middle term. The conclusion is therefore 
said to be mediated^ and the process itself is sometimes called 
mediate reasoning. 

It will be interesting to compare what has just been said regard- 
ing the function of the middle term, with what has been previously 
stated regarding the nature of inference. When we infer one fact 
from another, it was said, we do so by discovering some identical link 
or connecting thread which unites both. Wo may say that to infer 
is to see that, in virtue of some identical link which our thought has 
brought to light, the two facts, or groups of facts, are in a certain 
sense identical. Now the middle term in a syllogism is just the 
explicit statement of the nature of this identical link. It is true that 
in the syllogism we seem to be operating with words or terms rather 
than with the thought-process itself. When we go behind the 
external connection of the terms, however, we can see that the 
middle term represents the universal principle, by means of which 
the conclusion is reached. In the example given above, for in- 
stance, we reason that the whale, heing a mammal^ is a vertebrate. 

The terms which enter into the conclusion of a syllogism 
are sometimes called the Extremes^ as opposed to the middle 
term. Of the Extremes, the predicate of the conclusion is 
known as the Major Term, and the subject of the conclusion as 
the Minor Term. The premise which contains the major 
term is called the Major Premise, and stands first when 
the syllogism is arranged in logical form. The Minor Premise 
on the other hand, is the premise which contains the minor 
term, and it stands second in the arrangement of the syllogism. 
The propositions of which the syllogism is composed may occur, 
however, in any order in actual reasoning; either premise, or 



§ 30. Tlie Rules of the Syllogism 115 

even the conclusion, may stand first. To arrange an argu- 
ment, therefore, it is necessary to determine which is the major, 
and which is the minor premise. This can be done most 
readily by turning to the conclusion, and distinguishing the 
major and minor terms. For example, take the syllogism : — • 

The whale suckles its young, 
No fish suckles its young, 
Therefore the whale is not a fish. 

By turning to the conclusion we see that ^ fish ' (being the 
broader term and therefore naturally predicate) is the major 
term. The proposition which contains this term, ^ no fish 
suckles its young, ' is, therefore, the major premise, and should 
stand first. Before proceeding to examine the syllogism 
further it would be necessary to arrange it as follows : — 

No fish is an animal which suckles its young, 
The whale is an animal which suckles its young, 
Therefore the whale is not a fish. 

§ 30. The Rules of the Syllogism. — It is customary to give 
a number of rules or canons to which the syllogism must con- 
form in order to yield valid conclusions. We shall first enu- 
merate the rules, and afterwards remark on their meaning 
and importance. 

(i) In every syllogism there should be three, and only three, 
terms, and these terms must be used throughout in the same 
sense. 

The terms, as we have already remarked, are known as the 
major term, the middle term, and the minor term. 

(2) Every syllogism contains three, and only three, 
propositions. 



Ii6 The Syllogism 

These are called the major premise, minor premise, and 
conclusion. 

(3) The middle term must be distributed in at least one of 
the premises. , 

(4) No term i&iist' be distributed in the conclusion which 
was not distributed in one of the premises. 

(5) From negative premises nothing can be inferred. 

(6) If one premise be negati ve, the conclusion must be nega- 
tive; and, conversely, to prove a negative conclusion one of 
the premises must be negative. 

As a consequence of the above rules there result two addi- 
tional canons which may be set down here. 

(7) No conclusion can be drawn from two particular 
premises. 

(8) If one of the premises be particular, the conclusion 
must be particular. 

The reason for the first and second rules will be evident 
from what has been already said about the structure of the 
syllogism. We saw that a logical argument is a process of 
comparison; that two terms are united through comparing 
them with a common or middle term. If the meaning of the 
terms does not remain fixed, there are more than three terms, 
and no comparison is possible. The second rule follows as 
a corollary from the first. 

The third rule, that the middle term must be distributed 
once, at least, is extremely important, and its necessity will be 
readily perceived. For, since the middle term is the standard 
of comparison, it must be used in at least one premise in its 
universal extent. Otherwise we might compare the major 
term with one part of it, and the minor term with another part. 
Such a comparison would of course not warrant us in either 



§ 30- The Rules of the Syllogism 117 

affirming or denying the connection of these terms in the con- 
clusion. For example, the two propositions, — 
Sedimentary rocks are stratified substances, 
Some metamorphic rocks are stratified substances, 

do not distribute the middle term, ' stratified substances, ' at 
all, being both affirmative propositions. It is clear that the 




Fig. 6. 
term, ' sedimentary rocks, ' agrees with one part of the strati- 
fied substances, and ' metamorphic rocks ' with another part. 
We are, therefore, not able to infer that ^ some metamorphic 
rocks are sedimentary rocks.' This may be clearly shown by 
representing the propositions by Euler's method of circles as 
in Fig. 6. We know from the second proposition that the circle 
representing ^ metamorphic rocks ' falls partly within the 
circle of ^ stratified substances.' But it is impossible to deter- 
mine from the statement whether it corresponds at all with 
the circle of sedimentary rocks, or falls, as in the figure, 
entirely without it. 

The fourth rule states that no term naust be distributed in the 
conclusion which was not distributed in one of the premises. 
That is, the conclusion must be proved hy means of the prem- 
ises, and no term which was not employed in its universal 



ii8 The Syllogism 

signification in the premises can, therefore, be used universally 
or distributively in the conclusion. This rule may be violated 
by using either the major or the minor term in a wider sense 
in the conclusion than in the premise in which it occurs. The 
resulting fallacies are then known as the Illicit Process of the 
major and minor terms respectively. As an illustration of the 
illicit process of the major term, we may consider the following 
argument:- ^ ^ ^ J ^^ 

All ratipnal beings are i^esponsible for their actions, 
Brutes are not rational beings, 

Therefore brutes are not responsible Mi their actions. 

It will be at once se^n that the major term, ' beings responsible 
for their actions,' is distributed in the conclusion, but was not 
distributed when it appeared as the predicate of an affirmative 
proposition in the major premise. The fallacious nature of this 
argument may also be shown by representing the proposition 
by circles. 
The illicit process of the minor term is usually more easily 

detected. We may take as an example of this fallacy : — ; 

i \ I " 

All good citizens are ready to defend theil* 'country, 

All good citizens are persons who vote regularly at elections, 

Therefore all who vote regularly at elections are ready to defend 
their country. 

It is clear that the minor term, ' persons who vote regularly at 
elections,' is undistributed when used as the predicate of the 
minor premise. In the conclusion, however, it is wrongly 
taken universally, and it is this unwarranted extension to which 
the name of illicit minor is given. Students are advised to 
draw circles to illustrate the nature of this fallacy. 



§ 30. TJie Rules of the Syllogism *II9 

The fifth and sixth rules have reference to negative premises. 
It is not difficult to understand why two negative premises can- 
not yield any conclusion. For, from the fact that S and P are 
both excluded from M, we can conclude nothing regarding 
their relation to each other. Two negative premises afford us 
no standard by means of which we can determine anything con- 
cerning the relation of major and minor terms. Again, where 
one premise is negative and the other affirmative, it is asserted 
that, of the major and minor terms, one agrees, and the other 
does not agree, with the middle term. The necessary inference 
from these premises, then, is that major and minor terms do 
not agree with each other. That is, the conclusion must be 
negative. - 

It is worth noticing that it is sometimes possible to obtain a 
conclusion from premises which are both negative in form. For 
example: — 

No one who is not thoroughly upright is to be trusted, 
This man is not thoroughly upright. 

Therefore this man is not to be trusted. 

In this example, although the form of both premises is negative, 
the minor premise supplies a positive basis for argument, and is 
really affirmative in character. Or we may say that the ^ not ' in 
the predicate of the minor premise belongs to the predicate, and 
not to the copula. The proposition may therefore be said to affirm, 
rather than to deny. 

The seventh and eighth rules, v/hich refer to particular premises 
can be proved by considering separately all the possible combi- 
nations of premises. If this is done, it will be found that these rules 
are direct corollaries from the third and fourth, which are con- 
cerned with the proper distribution of terms. It is impossible 



I20* The Syllogism 

to secure the necessary distribution with two particular premises; 
for either the distribution of the middle term will not be provided 
for, or if this has been secured by means of a negative premise, 
the conclusion will show a case of the illicit major term. By means 
of the same rules, it may be shown that a particular premise 
always requires a particular conclusion. The truth of these 
two subordinate canons also may be readily shown by the use of 
circles. 

§ 31. The Figures of the Syllogism. — We have seen what 
an important part the middle term plays in the syllogism. It 
constitutes the mediating link between the major and minor 
terms, and makes possible their union. Now upon the position 
of the middle term in the premises depends the Figure of the 
syllogism. There are four possible arrangements of the 
middle term in the two premises, and therefore four figures of 
the syllogism. If we let P represent the major term, S the 
minor, and M the middle term, the form of the different fig- 
ures may be represented as follows: — 

First Figure Second Figure 

M— P P— M 

S — M S — M 



/. S — P .-. S — P 

Third Figure Fourth Figure 

M — P P — M 

M— S M— S 



.-. S — P .\S — P 

In the first figure, the middle term is the subject of the 
major premise, and the predicate of the minor premise. 

In the second figure, the middle term is predicate of both 
major and minor premises. 



§ 31- The Figures of the Syllogism 121 

The third figure has the middle term as the subject of both 
premises. 

In the fourth figure, the middle term occupies just the oppo- 
site position in the two premises to that which it holds in 
the first figure ; i.e, it is the predicate of the major premise, 
and the subject of the minor premise. 

u ^ ^ ^ ' 




1 ■ J ^ 



u 






-^ 






V 










i^'" 










\\v 



CHAPTER IX 

THE VALID MOODS AND THE REDUCTION OF FIGURES 

§ 32. The Moods of the Syllogism. — By the Mood of a 
syllogism we mean the combination of propositions A, E, I, and 
O, which goes to make it up. Thus, when a syllogism is made 
up of three universal affirmative propositions, we speak of it 
as the mood AAA; if it is composed of a universal negative, a 
particular affirmative, and a particular negative proposition, 
we name it the mood EIO. 

Every syllogism, as has been already stated, is made up of 
some arrangement of the four propositions A, E, I, O, taken 
three at a time. Now, there are in all sixty-four possible per- 
mutations of these four propositions taken three at a time. 
We might then write out these sixty-four moods, and proceed 
to determine which of them are valid. But this would be a 
long and somewhat tedious undertaking. Moreover, if we 
can determine which are the valid combinations of premises, 
we can draw the proper conclusions for ourselves. Since, 
then, there are but two premises in each syllogism, we shall 
have to deal only with the possible permutations of A, E, I, 
and O, taken two at a time, or with sixteen combinations in 
all. 

The following, then, are the only possible ways in which the 

propositions A, E, I, and O can be arranged as premises.; — 

122 



§ 33* '^^^ Special Canons of the Four Figures 123 



AA 


EA 


lA 


OA 


AE 


EE 


IE 


-OE 


AI 


EI 


II 


01 


AO 


EO 


10 


00 



Some of these premises, however, cannot yield conclusions, 
since they plainly violate certain rules of the syllogism. The 
combinations of negative premises EE, EO, OE, and 00 can 
be at once struck out. Again, since no conclusion follows from 
two particular premises, we can eliminate II, 10, and 01. 
There remain, then, for further consideration the combina- 
tions : — 

AA EA lA OA 

AE — IE — 

AI EI — — 

AO — — — 

At this point we must recall the fact that every argument 
must belong to one of the four figures. We must now there- 
fore ask this question: Which of the above combinations of 
premises will yield valid conclusions in the first, second, third, 
and fourth figures, respectively ? By examining the form of 
the syllogism in each of these figures, we shall be able to dis- 
cover what conditions must be fulfilled in each case, and to lay 
down special canons for each figure. We shall first proceed 
to state and prove the special canons of the different figures. 
It will not, however, be necessary for the student to commit 
these rules to memory, as he can always derive them for him- 
self by a consideration of the form of the argument in the 
different figures. 

§ 33. The Special Canons of the Four Figures. — In the 
first figure^ the minor premise must be affirmative, and the major 
premise universal. 



124 The Valid Moods and the Reduction of Figures 
The first figure is of the form : — 



S — M 



.-.S 



To show that the minor premise is affirmative, we employ the 
indirect method of proof. Let us suppose that the minor 
premise is not affirmative, but negative. Then since one prem- 
ise is negative, the conclusion must be negative. But if the 
conclusion is a negative proposition, its predicate, P, must be 
distributed. Any term which is distributed in the conclusion 
must, however, have been distributed when it was used in the 
premise. P must be distributed, therefore, as the predicate of 
the major premise. But since negative propositions alone 
distribute their predicates, the major premise, M — P, must 
be negative. But by hypothesis the minor premise, S — M, 
is negative. We have, therefore, two negative premises, 
which is impossible. Our supposition, that the minor 
premise is negative, is therefore false; or, in other words, the 
minor premise must be affirmative. 

This having been established, we can very easily prove that 
the major premise must be universal. For the middle term, 
M, must be distributed in at least one of the premises. But 
it is not distributed in the minor premise, for it is there the 
predicate of an affirmative proposition. It must, therefore, 
be distributed as the subject of the major premise, that is, the 
major premise must be universal. 

If we turn now to the second figure, we shall find that the 
following rules may be deduced from a consideration of its 
form : — 



§ 33- The Special Canons of the Foicr Figm^es 125 

(i) One premise must be negative, [and the conclusion there- 
fore negative/ 

(2) The major premise must be universal, 
The second figure is in the form : — 

P— M 
S— M 



The reason for the first rule is at once evident. If one 
premise is not negative, the middle term, M, is not distrib- 
uted, and no conclusion is therefore possible. The only 
means of securing distribution of the middle term in the 
second figure is by means of a negative premise. And if 
one premise is negative, it of course follows that the conclu- 
sion must be negative. 

This having been established, the proof of rule 2 follows 
almost immediately. For, since the conclusion is negative, 
its predicate, P, must be distributed. And since P is distrib- 
uted in the conclusion, it must have been used distributively 
when it occurred as the subject of the major premise, or, in 
other words, the major premise must be universal. 

The third figure is of the form : — 



M— P 

^^'M— S 



u 



From an analysis of this, the two following rules may be 
obtained : — 

(i) The minor premise must be affirmative, 

(2) The conclusion must be particular. 

The minor premise is here shown to be affirmative by 
the method employed in proving the same rule in the first 



126 The Valid Moods ajtd the Reduction of Figures 

figure. That is, we suppose the minor premise negative, 
and show that, as a result of this hypothesis, the conclusion 
is negative, and the major term distributed. It follows, 
then, that this term must be distributed as the predicate 
of the major premise. But this could happen only if this 
premise were negative. The hypothesis that the minor 
premise is negative thus leads to the absurdity of two nega- 
tive premises. The conclusion that the opposite is true^ 
that the minor premise is affirmative, is therefore proved 
indirectly. 

Since the minor premise is affirmative, its predicate 
S is undistributed. This term must therefore be used in 
an undistributed, i,e,^ particular sense in the conclusion. 
And, as this term forms its subject, the conclusion is par- 
ticular. 

In the fourth figure the terms are arranged in the follow- 
ing way: — 

P — M 

M— S 
.-. S— P 

From a consideration of the form of this figure we can obtain 
the following special canons: — 

(i) If either premise he negative^ the major premise must 
be universal, 

(2) If the major premise he affirmative, the minor must he 
universal, 

(3) If the minor premise he affirmative, the conclusion must 
he particular. 

The student will be able to prove these canons for himself 
by applying the rules of the syllogism in the same way as 
has been done in the proofs already given. 



§ 34- ^^^ Determination of the Valid Moods 127 

§ 34. The Determination of the Valid Moods in Each of 
the Figures. — We have now to apply these special canons 
in order to determine what moods are valid in each of the 
four figures. It has already been shown (p. 122) that the 
premises which are not excluded by the general rules of the 
syllogism are: — 

AA EA lA) OA 

AE — IE — 

AI EI — — 

AO — -- — 

Now we have proved that in the first figure the major premise 
must be universal, and the minor affirmative. The only 
combinations of premises which will stand these tests are, 
AA, EA, AI, and EI. Drawing the proper conclusion in 
each case, we have as the four valid moods of the first 
figure: — 

AAA, EAE, All, EIO. 

It will be noticed that the first figure enables us to obtain 
as conclusion any one of the four logical propositions 
A, E, I, and O. 

The special canons of the second figure state that the 
major premise must be universal, and one premise negative. 
Selecting the combinations of premises which fulfil these 
conditions, we obtain EA, AE, EI, and AO. These give, 
when the conclusions have been drawn, the following four 
moods of the second figure: — 

EAE, AEE, EIO, AOO. 

By means of the second figure, therefore, we are able to 
establish the truth only of the negative propositions, E and O. 



128 The Valid Moods a7id the Reduction of Figures 

In the third figure the minor premise must be affirma- 
tive, and the conclusion particular. Taking all the com- 
binations in which the minor is affirmative, there result, 
AA, lA, AI, EA, OA, EI. It must be remembered that 
the third figure yields only particular conclusions, even 
where both premises are universal. The valid moods in 
this figure are therefore as follows : — 

AAI, lAI, All, EAO, OAO, EIO. 

The canons of the fourth figure, which have to do with 
the premises, state that where either premise is negative, a 
universal major is necessary, and that an affirmative major 
premise must be accompanied by a universal minor. The 
combinations of propositions which fulfil these conditions 
are AA, AE, lA, EA, and EI. In drawing conclusions 
from these premises, however, it is necessary to pay attention 
to the third canon of this figure, which states that where 
the minor premise is affirmative, the conclusion must be 
particular. Accordingly, the valid moods of this figure 
may now be written : — 

AAI, AEE, lAI, EAO, EIO. 

Here we are able to obtain a universal negative as a conclu- 
sion, but not a universal affirmative. It is interesting to 
notice that the first figure alone enables us to prove a propo- 
sition of the form A. 

It may also be pointed out that the combination [I E], 
although not excluded by the general rules of the syllogism, 
cannot be used at all as a premise, since it violates the canons 
of all four figures. There remain in all, then, nineteen 
valid moods of the syllogism, — four in the first figure, 



§ 35- ^^^^ Mnemonic Lines 129 

four in the second, six in the third, and five in the fourth 
figure. 

§ 35. The Mnemonic Lines. — It is not necessary to 
commit to memory the vahd moods in each figure. By 
applying the general rules of the syllogism to the figure 
in question, the student will be able to determine for himself 
in every case whether or not an argument is valid. The 
Latin Schoolmen in the thirteenth century, however, in- 
vented a system of curious mnemonic verses for the pur- 
pose of rendering it easy to remember the valid moods 
in each figure. Although it is not necessary for the student 
to burden his memory with these barbarous names, it is 
interesting to understand the use of the lines: — 

Barbara, Celarent, Darii, Ferioque prioris; 
Cesare, Camestres, Festino, Baroko, secundae; 
Tertia, Darapti, Disamis, Datisi, Felapton, 
Bokardo, Ferison, habet ; Quarta insuper addit 
Bramantip, Camenes, Dimaris, Fesapo, Fresison. 

The words printed in ordinary type are real Latin words, 
indicating that the four moods represented by Barbara, 
Celarent, Darii, and Ferio are the valid moods of the first 
figure, that the next four are valid in the second figure, 
that the third figure has six valid moods represented 
by as many artificial names, and that the fourth figure 
adds five more. Each word represents a mood, the vowels 
A, E, I, and O indicating the quality and quantity of the 
propositions which go to compose them. Thus, Barbara 
signifies the mood of the first figure which is made up of 
three universal affirmative propositions AAA; Cesare, a 
mood of the second figure, composed of the three proposi- 



130 The Valid Moods and the Reduction of Figures 

tions EAE. These lines, then, sum up the results reached 
on pages 126-127 regarding the vahd moods in each figure. 
But certain consonants in these mnemonic words also 
indicate how arguments in the second, third, or fourth 
figures may be changed to the form of the first figure. The 
first figure was called by Aristotle the perfect figure, and 
the second and third the imperfect figures, since he did not 
regard an argument in these forms as so direct and con- 
vincing as one of the first-mentioned type. The fourth 
figure was not recognized by Aristotle, but is said to have 
been introduced into logic by Galen, the celebrated teacher 
of medicine, who hved in the latter half of the second century. ^ 
If we consider an example of this figure, the reason for re- 
fusing it an equal rank with the other three will appear: — 

The whale is a mammal, 

All manimals are vertebrates, >\ 

Therefore some vertebrates are whales. 

It is plain that the conclusion of this argument is some- 
what strained. That is, it would be more natural to obtain 
the conclusion ' ^ whales are vertebrates,' than to infer that 
^ some vertebrates are whales ' ; for this statement seems 
to make the species, or less inclusive term, the predicate of 
the genus, or wider term. It was for this reason, apparently, 
that Aristotle omitted this figure, as improperly making 
the rear major term a minor, and the real minor a major, 
and so stating in a less adequate way an argument which 
could have been better formulated in the first figure. 

The process of changing an argument from one of the 
so-called imperfect figures to that of the first figure is known 
as Reduction. And, as we have said, these curious but 



§ 35- ^^^-^ Mnemonic Lines 131 

ingenious mnemonic words give rules for carrying out this 
process. For example, s indicates that the proposition 
represented by the preceding vowel is to be converted simply. 
Thus an argument in the second figure of the mood Cesare 
is changed to Celarent in the first figure, by converting the 
major premise simply. Again, p denotes that the preced- 
ing vowel is to be converted by limitation, or per accidens ; 
m is supposed to stand for mutare^ and indicates that the 
premises are to be transposed; k, which is used in the moods 
Baroko and Bokardo, shows that an indirect method of 
proof or reduction is necessary to reduce the arguments 
to the first figure. 

-Further, the initial consonants of the moods of the imper- 
fect figures correspond with those of the moods in the first 
figures, to which they can be reduced. Cesare and Cames- 
tres of the second figure, for example, and Camenes of the 
fourth are reducible to Celarent; and, similarly, Festino, Felap- 
ton, Fesapo, and Fresison may all be reduced to Ferio. 

The student who understands the structure of the syllogism will 
be able to arrange an argument in one figure or another, as may be 
most convenient, v/ithout the aid of any mechanical rules. It may 
be interesting, however, to give a single example for the sake of 
illustrating the workings of this most ingenious device. Let us take 
the following argument in the second figure of the mood AEE, or 
Camestres : — 

All members of the class are prepared for the examination, 
No idle persons are prepared for the examination, 

Therefore no idle persons are members of the class. 

Now the m in Camestres shows that the major and minor premises 
are to be transposed ; the first s indicates that the minor premise is 



132 The Valid Moods and the Reduction of Figures 

to be converted, and the second that the same process must be 
performed on the conclusion. 

Converting the minor premise and transposing, we obtain: — 

No persons prepared for the examination are idle, 

All members of the class are prepared for the examination. 

Converting the conclusion, 

Therefore no members of the class are idle persons. 

This result, as will at once be seen, is an argument in the first 
figure of the mood EAE, or Celarent. 

REFERENCES 

Sir W. Hamilton, Lectures on Logic. Lectures XX., XXL 
A. Bain, Logic ^ Part First, Deduction, Bk. 11. , Ch. I. 

Note. — It would be interesting to work out, in connection with 
the various forms of inductive reasoning treated in Part 11. , the organic 
relation of the syllogistic figures, and their natural applicability to 
various purposes of argument. This task, however, seemed to lie beyond 
the proper limits of this book. All of the investigations on this point start 
from Hegel's treatment in the second part of the Wissenschaft der Logik 
(Werke, Bd. 5, pp. 115 ff.). Those interested in this subject may consult 
W. T. Harris, T/^g Psychologic Foundations of Education ^ Ch. IX.-XL, 
and the same author's Logic oj Hegel. See also B. Bosanquet, Logic, 
Vol. n., pp. 44 ff., 88 ff., and The Essentials oJLogic^ Lecture X. ; H. W. B. 
Joseph, An Introduction to Logic, Ch. XIV. 



CHAPTER X 

ABBREVIATED AND IRREGULAR FORMS OF ARGUMENT 

§ 36. Enthymemes. — The term ' enthymeme ' seems to 
have been used by Aristotle for an argument from signs or 
from HkeHhood, without complete proof. From this sense 
of logical incompleteness, the name has come to be applied 
in modern times to an argument in which some part is omitted. 
We have already noticed, in dealing with the syllogism 
(§ 10), that one premise is often omitted. Indeed, it is but 
seldom in ordinary reasoning that we arrange our arguments 
in the strict syllogistic form. We hurry on from one fact to 
another in our thinking without stopping to make all the 
steps definite and explicit. We feel it to be a waste of time, 
and a trial to the patience, to express what is clearly obvious, 
and so we press on to the conclusion which is, for the time 
being, the central point of interest. 

But the more rapid and abbreviated the reasoning, the 
more necessary is it to keep a clear head, and to under- 
stand what conclusion is aimed at, and what premises are 
assumed in the argument. To bring to light the hidden 
assumption upon which an argument is based, is often 
the best means of refuting it. 

Enthymemes are sometimes said to be of the first, second, 
or third order, according as the major premise, the minor 
premise, or the conclusion is wanting. As a matter of fact, 

^33 



134 Abbreviated and Irregular Forms of Argument 

an enthymeme of the third order is a rhetorical device used 
to call special attention to a conclusion which is perfectly 
obvious, although suppressed. Thus, for example, ^ all 
boasters are cowards, and we have had proofs that A is a 
boaster.' Here the conclusion is at once obvious, and is 
even more prominent than if it were actually expressed. 
It is usually easy to complete an enthymeme. If the 
conclusion and one premise are given, the three terms of 
the syllogism are already expressed. For the conclusion 
contains the major term and the minor term; and one of 
these again, in combination with the middle term, is found 
in the given premise. From these data, then, it will not 
be difficult to construct the suppressed premise. When 
the premises are given without the conclusion, there is no 
way of determining, except from the order, which is major 
and which is minor. It is therefore necessary to assume 
that they are already arranged in proper logical order, and 
that the subject of the conclusion, or minor term, is to be 
found in the second premise, and the predicate of the conclu- 
sion, or major term, in the first premise. 

§ 37. Prosyllogisms and Episyllogisms. — In deductive 
reasoning it is often necessary to carry on the argument 
through several syllogisms, using the conclusion first reached 
as a premise in the following syllogism. For example, we 
may argue: — 

All B is A 

All C is B 



All C Is A. 
But all D is C 



.-. All D is A. 



§ 37- Prosyllogisms and Episyllogisms 135 

It is clear that we have here two arguments in the first 
figure. The first is called the Prosyllogism, and the latter 
the Episyllogism. If the argument were carried on further, 
so as to include three or more syllogisms, the second would 
form the Prosyllogism with respect to the third, while the 
third would be the Episyllogism of the second. A concrete 
example of this kind of reasoning may now be given: — 

All timid men are suspicious, 
All superstitious men are timid, 

Therefore all superstitious men are suspicious, 
But some educated men are superstitious. 

Therefore some educated men are suspicious. 

It will be noticed that in these examples the argument advances 
from the premises of the Prosyllogism, to the conclusion of the 
Episyllogism. It proceeds, that is to say, in a forward direction, 
developing the consequences of the premises which form its starting 
point. This mode of investigation is therefore called the Progres- 
sive or Synthetic^ since it goes steadily forward building up its results 
as it advances. To state the same thing in different words, we may 
say that the Progressive or Synthetic method advances from the 
conditions to what is conditioned, from causes to eff'ects. 

But it is often necessary to proceed in the opposite way. We 
have often to go back and show the grounds upon which our prem- 
ises rest, instead of going forward to show what consequences 
follow from them. And when we do this we proceed Regressively 
or Analytically. To take an example which will illustrate both 
ways of proceeding: — 

No man is infallible, for no man is omniscient, 
Aristotle was a man, 

Therefore Arir tie was not infallible. 



136 Abbreviated and Irregular Forms of Argument 

In advancing from the premises to the conclusion in this argument 
our procedure is progressive or synthetic. Instead of reasoning out 
the consequences of the premises, however, we may go back and 
show the grounds upon which the major prenaise rests. It is evident 
that this premise is itself the conclusion of a syllogism which may 
be expressed as follows : — 

All infallible beings are omniscient, 
No man is omniscient, 



Therefore no man is infallible. 

The regressive method goes backward from conclusions to premises, 
or from the conditioned to its necessary conditions. In scientific 
investigation it reasons from effects to causes, while the synthetic 
method advances from causes to effects. 

§ 38. Sorites, or Chains of Reasoning. — A Sorites is 
an abbreviated form of syllogistic reasoning in which a 
subject and predicate are united by means of several inter- 
mediate terms. Such a train of reasoning represents sev- 
eral acts of comparison, and therefore several syllogistic 
steps. But instead of stopping to draw the conclusion at 
each stage, the sorites continues the processes of compari- 
son, and only sums up its results at the close. We may 
define the sorites, therefore, as a series of prosyllogisms and 
episyllogisms in which all of the conclusions, except the last, 
are suppressed. It is usually stated in the following form : — 

All A is B 

All B is C 

^ All C is D 

All D is E 



All A is E, 



§ 38. Sorites^ or Chains of Reasoning 137 

It is evident that this train of reasoning fully expressed 
is equivalent to the following three syllogisms: — 

First Syllogism Second Syllogism Third Syllogism 

AllBisC AUCisD All D is E 

All A is B All A is C (i) All A is D (2) 



.-. All A is C (i). .-. All A is D (2). .-. All A is E (3). 

There are two rules to be observed in using this form 
of the sorites: (i) The first premise may be particular, all the 
others must be universal ; (2) The last premise may be neg- 
ative, all the others must be affirmative. It is evident 
from an examination of the syllogisms given above that if 
any premise except the first were particular, the fallacy 
of undistributed middle would be committed. For, in that 
case, the middle term in one of the syllogisms would be the 
subject of a particular proposition, and the predicate of an 
affirmative proposition. And if any premise but the last 
were negative, the major term in the syllogism following 
that in which this occurred would be distributed in the con- 
clusion without having been distributed in the major premise. 
We may now give some concrete examples of this kind of 
reasoning: — 

Misfortunes sometimes are circumstances tending to improve 
the character, 

Circumstances tending to improve the character are promoters 
of happiness, 

What promotes happiness is good, 

Therefore misfortunes are sometimes good. 

In some cases the different terms of an argument of this 
kind are expressed in the form of hypothetical propositions. 



138 Abbreviated and Irregular Forms of Argtiment 

Thus, for example, we might argue: If a man is avaricious, 
he desires more than he possesses; if he desires more 
than he possesses, he is discontented; if he is discontented, 
he is unhappy ; therefore, if a man is avaricious, he is 
unhappy. This argument is hypothetical in form only, 
and may be easily reduced to categorical type as follows: — 

if> -A. 

An avaricious man is one who desires more than he possesses, 
A man who desires more than he possesses is discontented, 
A discontented man is unhappy, 

Therefore an avaricious man is unhappy. 

It will be noticed that the subject of the first premise 
in this form of argument is taken as the subject of the 
conclusion, and that the predicate of the conclusion is the 
predicate of the last premise. This is usually called the 
Aristotelian sorites. But there is another form which 
unites in the conclusion the subject of the last premise, 
and the predicate of the first, and which is known as the 
Goclenian sorites.^ This may be thus represented: — 

All A is B 
All C is A 
All D is C 
All E is D 



.-. All E is B. 
Since B is the predicate of the conclusion, the premise in 
which it appears is always to be regarded as the major. 
As a result of this, it is to be noticed that the suppressed 
conclusions in this argument form the major premise of 
the following syllogism, instead of the minor premise as in 

^Rudolf Goclenius (1547-1628), Professor at Marburg, first explained 
this form in his Isagoge in Organum AristotliSy 1598. 



§ 39- Irregular Arguments 139 

the Aristotelian sorites. We may, therefore, expand the 
reasoning into the three following syllogisms: — 

First Syllogism Second Syllogism Third Syllogism 

All A is B All C is B All D is B 

All C is A All D is C All E is D 



.-. All C is B. .-. All D is B. /. All E is B. 

A little consideration of the form of these syllogisms will lead 
the student to see that the rules given for the Aristotelian 
sorites must be here reversed. In both forms of the sorites 
there cannot be more than one negative premise, nor more 
than one particular premise. In the Aristotelian form, no 
premise except the last can be negative, and no premise 
except the first particular. In the Goclenian sorites, on the 
other hand, the single premise which can be negative 
is the first, and it is the last alone which may be particular. 
§ 39. Irregular Arguments. — There are a large number 
of arguments employed in everyday life which are valid and 
convincing, and yet which cannot be reduced to the syllogistic 
form. The difficulty with these arguments is that they appear 
to have four terms, at least in the form in which they are most 
naturally stated. We may discuss such irregular forms of 
reasoning under three headings: (i) Arguments which deal 
with the relations of things in time and space, or with their 
quantitative determinations; (2) arguments a/(9r/wi; (3) ar- 
guments which are largely verbal in character, and may be 
said to depend upon the principle of substitution. 

(i) As an example of the first class of argument we may 
take the following : — 

A is greater than B, 

B is greater than C, 



Therefore A is still greater than C. 



140 Abbreviated and Irregular Forms of Argument 

It is obvious that, although we have here four terms, the con- 
clusion is valid, and the form of argument perfectly convincing. 
The truth seems to be that in reasoning about quantities we do 
not proceed upon the syllogistic principle of the inclusion and 
exclusion of terms. But knowing the continuous nature of 
quantity, we take as our principle that, ^ what is greater than 
that which is greater than another is a fortiori greater than 
that other.' It would not, however, make the matter any 
clearer to write this as our major premise, and bring the real 
argument under it in this way : — 

What is greater than that which is greater than another is 
still greater than that other, 

A is that which is greater than that which is greater than C, 

Therefore A is still greater than C. 

What we have here given as the major premise is simply a 
statement of the nature of quantity, not a premise from which 
the conclusion is derived. We find the same irregularity in 
arguments referring to the relations of things in space and 
time: — 

A is situated to the east of B, 

B is situated to the east of C, 



Therefore A is to the east of C. 



In spite of the formal deficiency of four terms the argument is 
valid. It will be observed, too, that it is in virtue of the com- 
parison of the position of A and of C with that of B, that these 
relative positions have been determined. The principle upon 
which we proceed may be said to be that, ^ what is to the east 
of B is to the east of that which B is to the east of.' Or per- 
haps it would be truer to fact to say that we proceed in such 



§ 39- Iri'egiilar Arguments 141 

cases upon what we know regarding the nature of space, 
and the relations of objects in space. 

(2) A fortiori arguments proceed to establish a conclu- 
sion by showing that the facts and reasons which support it 
are more certain or stronger than those which support an- 
other conclusion that is unquestioned, or generally accepted. 
They are frequent in dealing with questions of time, space, 
quantity, and degrees of quality, and all three of the ex- 
amples just given may be regarded as coming under this 
head. In fact, we may say that in such matters, whenever 
the relation involved is not one of contemporaneousness 
in time, coincidence in space, or equality in quantity, or 
degree of quality, any argument naturally falls into the 
a fortiori form. The reason for putting this form into a class 
by itself is that it is very often employed outside of these fields. 
To illustrate the two ways in which it is used, for proof and 
disproof respectively, let us compare a possible argument ad- 
dressed by a vivisect ionist to a meat-eater with one urged upon 
an anti-vivisectionist by a vegetarian: — 

You admit that it is right to kill and use animals for food, 
This is less needful than to kill and use them to discover the 
causes and remedies of diseases, 

How much more, then, should you admit that vivisection is right. 

(2) 

You do not think that it is right to kill animals for vivisection, 
Yet this is more needful than to kill them for food, 

How much less, then, should you hold that it is right to kill them 
for food, or, How much more should you deny, etc. 

Such arguments as these seem always to involve a compar- 
ison of the grounds on which certain conclusions may be jus- 



142 Abbreviated and Irregular Forms of Argument 

tified, when such grounds can be ranked in order of logical 
cogency. In the one case, it is urged that since the reason for 
the conckision advocated is stronger than one which it is ad- 
mitted does estabhsh a certain proposition, the conclusion in 
question must, therefore, be regarded as even more firmly es- 
tablished; in the other, as the reason for holding the principle 
attacked is weaker than that which is regarded as insufficient 
to justify another principle, it is held that the first principle is 
still more obviously false than that already denied, or that 
there is more reason to deny it than there is to deny the other. 
Hence the name argumentum a fortiorij ^ argument from, or 
by, the stronger,' (^ reason' being understood). 

(3) The third class of irregular arguments is largely 
verbal in character, and may be dealt with very briefly. As 
an example we may consider: — 

Men are willing to risk their lives for gold, 

Gold cannot buy happiness, 

Therefore men are willing to risk their lives for what cannot buy 
happiness. 

It is doubtful, I think, whether these propositions represent 
any real inference. The whole process may be regarded as a 
verbal substitution in the major premise of ^ what cannot buy 
happiness' for the word ^gold.' By a slight change in the 
form of the proposition, however, the argument may be ex- 
pressed as a regular syllogism of the third figure: — 

Gold is something for which men are willing to risk their lives, 

Gold cannot buy happiness, 

Therefore something which cannot buy happiness is something 
for which men are willing to risk their lives. 

Another example which also appears to be irregular at first 
sight is added: — 



§ 39- Irregular Arguments 143 

The men of the Middle Ages were ready to undertake any expe- 
dition where glory could be won, 

The crusades were expeditions in which glory could be won, 

The crusades, therefore, were readily undertaken by the men 
of the Middle Ages. 

This argument seems to be irregular in form only, and by a 
slight change in form may be expressed in the first figure: — 

All expeditions in which glory could be won were readily under- 
taken by the men of the Middle Ages, 

The crusades were expeditions in which glory could be won, 

Therefore the crusades were readily undertaken by the men of 
the Middle Ages. 

REFERENCES, 

Especially for § ;^^ 

W. S. Jevons, The Principles oj Science^ Introduction. 
F. H. Bradley, The Principles of Logic, pp. 348-360. 



CHAPTER XI 

HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS 

§ 40. The Hypothetical Syllogism. — We have hitherto 
been deahng with syllogisms composed entirely of categori- 
cal propositions, and have not referred to the use which is 
made of conditional propositions in reasoning. A conditional 
proposition is sometimes defined as the union of two cate- 
gorical propositions by means of a conjunction. It is the 
expression of an act of judgment which does not directly or 
unambiguously assert something of reality. We have already 
pointed out (§ 20) that there are two classes of conditional 
propositions : the hypothetical and the disjunctive, and corre- 
sponding to these we have the hypothetical and the disjunctive 
syllogism. The hypothetical syllogism has a hypothetical 
proposition as a major premise, and a categorical proposition 
as a minor premise. The disjunctive syllogism in the same 
way is composed of a disjunctive proposition as major, and 
a categorical proposition as minor, premise. In addition to 
these, we shall have to treat of another form of argument 
called the ^dilemma,' which is made up of hypothetical and 
disjunctive propositions. 

A hypothetical proposition does not assert directly the ex- 
istence of a fact, but states the connection between a supposi- 
tion or condition and its consequence. It is usually intro- 

144 



§ 40. Tlie Hypothetical Syllogism 145 

duced by some word or conjunctive phrase, like ^ if/ ^supposing/ 
or 'granted that'; as, e.g,, 'if he were to be trusted, we might 
give him the message'; 'suppose that A is B, then C is D.' 
The part of a hypothetical proposition which expresses the 
supposition or condition is known as the Antecedent; the 
clause stating the result is called the Consequent. Thus, in 
the proposition, ' he would write if he were well,' the consequent, 
'he would write,' is stated first, and the antecedent, ' if he were 
well,' follows. 

The hypothetical syllogism, as has been already remarked, 
has a hypothetical proposition as its major, and a categorical 
proposition as its minor, premise: — 

If justice is to prevail, his innocence will be proved, 
And justice will prevail, 

Therefore his innocence will be proved. 

It will be noticed that in this argument the minor premise 
affirms the antecedent^ and that, as a result, the conclusion 
affirms the consequent. This form is known as \h^ construc- 
tive hypothetical syllogism, or the modus ponens. 

In the following example it will be observed that the con- 
sequent is denied, and the conclusion obtained is therefore 

negative. 

If he were well, he would write, 

He has not written, 



Therefore he is not well. 



This is called the destructive hypothetical syllogism, or modus 
tollens. 

The rule of the hypothetical syllogism may therefore be 
stated as follows: Either affirm the antecedent or deny the 



146 Hypothetical and Disjunctive Arguments 

consequent. If we affirm the antecedent, i,e.^ declare that the 
condition exists, the consequent necessarily follows. And, on 
the other hand, if the consequent is declared to be non-existent, 
we are justified in denying that the condition is operative. 

The violation of these rules gives rise to the fallacies of 
denying the antecedent^ and of affirming the consequent. Thus, 
for example, we might argue : — 

If he were well, he would write, 
But he is not well. 



Therefore he will not write. 

Here the antecedent is denied, and the argument plainly false. 
For we cannot infer that his being well is the only condition 
under which he would write. We do not know, in other words, 
that the antecedent stated here is the only, or essential condition 
of the consequent. We know that if there is fire, there must 
be heat; but we cannot infer that there is no heat when no fire 
is present. Of course, if we can be certain that our antecedent 
expresses the essential condition, or real sine qua non of the 
consequent, we can go from the denial of the former to that of 
the latter. For example : — 

If a triangle is equilateral, it is also equiangular, 
This triangle is not equilateral, 

Therefore it is not equiangular. ^ 

Usually, however, when the hypothetical form of expression is 
employed, we cannot be certain that the antecedent expresses 
the sole, or essential condition, of the consequent. At the 
ordinary stages of knowledge we have to content ourselves 
with reasoning from antecedent conditions, without being able 
to show that no other condition is possible. 



§ 40- T^^^^ Hypothetical Syllogism 147 

To illustrate the fallacy of affirming the consequent, we may 
take the following example : — 

If perfect justice prevailed, the rich would not be permitted to 
rob the poor, 

But the rich are not permitted to rob the poor, 

Therefore perfect justice prevails. 

Here it will be noticed that the consequent states only one 
result of the prevalence of ' perfect justice.' Because the 
consequent is declared to exist, it by no means follows that it 
exists as a consequence of the operation of this condition. It 
is also worth noting in this example that the consequent of 
the major premise is negative. The minor premise which 
affirms the consequent also takes a negative form. To deny 
the consequent we should have to say, ^ the rich are permitted 
to rob the poor.' Or, to put the matter generally, it is nec- 
essary to remember that the affirmation of a negative propo- 
sition is expressed by a negative proposition, and that the 
denial of a negative — the negation of a negation — is, of 
course, positive in form. 

A type of hypothetical argument differing in form from the 
hypothetical syllogism is that in which premises and conclusion 
are a\l hypothetical propositions, as, for example : — 

If the tariff is increased, prices will rise. 

If prices rise, the majority of the people will be discontented, 
If the majority are discontented, the Republican party will be 
defeated at the next election, 

Therefore, if the tariff is increased, the Republican party will 
be defeated at the next election. 



148 Hypothetical and Disjunctive Arguments 

This is an hypothetical sorites, corresponding to the Aristotelian 
form of the categorical sorites, in that its conclusion unites the ante- 
cedent of the first premise with the consequent of the last. There 
are also hypothetical sorites which unite the antecedent of the last 
premise with the consequent of the first in their conclusion, and 
thus correspond to the Goclenian sorites. Such sorites are often 
hypothetical in form only, as has been pointed out in the preceding 
chapter, and when this is the case they may be reduced to cate- 
gorical syllogisms of the first figure, as in the example there 
given {Iz'S)' 

§41. Relation of Categoricf^ and Hypothetical Argu- 
ments. — It is evident that the form of the hypothetical 
syllogism is very different from that of the categorical. But, 
although this is the case, it must not be supposed that with the 
former we have passed to a new and wholly distinct type of 
reasoning. In hypothetical reasoning, as in categorical, it is 
the presence of a universal principle which enables us to bring 
into relation two facts which formerly stood apart. Indeed, in 
many cases, it is a matter of indifference in which form the 
argument is stated. Thus, we may argue in hypothetical 
form : — 

If a man is industrious, he will be successful, 
A is an industrious man, 

Therefore A will be successful. 

The same argument may, however, be expressed equally well 
in categorical form : — 

All industrious men will be successful, 
A is an industrious man. 



Therefore A will be successful. 



§ 41- Categorical and Hypothetical Arguments 149 

It is clear that, in spite of the different forms in which the 
argument is expressed, the reasoning is essentially the same in 
both cases. The middle term, or general principle which 
makes it possible to unite the subject and predicate of the con- 
clusion, in the hypothetical as well as in the categorical 
syllogism, is ^ industrious.' A will be successful, we argue, 
because he is industrious, and it is a rule that industrious men 
are successful. 

Moreover, if an argument is fallacious in one form, it w^ill 
also be fallacious when expressed in the other. The defects of 
an argument cannot be cured simply by a change in its form. 
When an hypothetical argument, in which the antecedent is 
denied, is expressed categorically, we have the fallacy of the 
illicit major term. Thus, to state the example of denying the 
antecedent given on page 146, we get: — 

The case of his being well is a case of his writing, 
The present is not a case of his being well, 

Therefore the present is not a case of his writing. 

Similarly, when an argument in which the consequent is 
affirmed is changed to the categorical form, the defect 
in the reasoning appears as the fallacy of undistributed 
middle: — 

If this tree is an oak, it will have rough bark and acorns, 
This tree has rough bark and acorns, 

Therefore it is an oak. 

When this argunlent is expressed in categorical form, it is at 
once clear that the middle term is not distributed in either the 
major or minor premise: — 



150 Hypothetical and Disjunctive Arguments 

All oak trees are trees having rough bark and acorns, 
This tree is a tree having rough bark and acorns, 

Therefore this tree is an oak. 

The change from the categorical to the hypothetical form 
of argument, then, does not imply any essential change in the 
nature of the reasoning process itself. Nevertheless, it is 
important to note that hypothetical propositions and hypothet- 
ical argum^ents emphasize one aspect of thinking, v^hich is 
entirely neglected by the theory of the categorical syllogism. 
When dealing v^ith the extension of terms (§ 16), we pointed 
out that every term, as actually used in a proposition, has both 
an extensive and an intensive function. That is, the terms of 
a proposition are employed both to name certain objects or 
groups of objects, and to connote or imply certain attributes 
or qualities. In the proposition, ^ these are oak trees,' the 
main purpose is to identify the trees given in perception v^ith 
the class of oak trees. When, on the other hand, v^e say, ^ igno- 
rant people are superstitious,' the proposition does not refer 
directly to any particular individuals, but states the necessary 
connection between ignorance and superstition. Although 
the existence of ignorant persons who are also superstitious is 
presupposed in the proposition, its most prominent function is 
to assert a connection of attributes which is wholly impersonal. 
We may perhaps say that, in spite of the categorical form, 
the proposition is essentially hypothetical in character. Its 
meaning might very well be expressed by the statement, ' if a 
man is ignorant, he is also superstitious.' What is here em- 
phasized is not the fact that ignorant persons exist, and are 
included in the class of superstitious persons, but rather the 
general law of the necessary connection of ignorance and 



§ 41- Categorical and Hypothetical Arguments 151 

superstition. The existence of individuals to whom the law 
applies is, of course, presupposed by the proposition. It is 
not, however, its main purpose to directly affirm their 
existence. 

We have reached, then, the following position: Every 
Judgment has two sides, or operates in two ways. On the 
one hand, it asserts the existence of individual things, and sets 
forth their qualities and relations to other things. But, at the 
same time, every judgment seeks to go beyond the particular 
case, and to read off a general law of the connection of attri- 
butes or qualities which shall be true universally. In singular 
and particular propositions, the categorical element — the 
direct assertion of the existence of particular objects — is 
most prominent, although even here the hint or suggestion of 
a general law is not altogether absent. When we reach the 
universal proposition, however, the reference to particular 
things is much less direct, and the meaning seems capable of 
expression in hypothetical form. 

Now in the chapters on the categorical syllogism this latter 
aspect of judgments has been left out of account. Proposi- 
tions were there interpreted as referring directly to objects, or 
classes of objects (cf. § 23). The proposition, S is P, for 
example, was taken to affirm that some definite object, or class 
of objects, S, falls within the class P. And the fact that it is 
possible to apply this theory shows that it represents one side 
of the truth. But the student must sometimes have felt that, 
in this procedure, the most important signification of the prop- 
osition is lost sight oi It seems absurd to say, for example, 
that in the proposition, ^ all material bodies gravitate,' the class 
of ^material bodies' is included in the wider class of ^things 
that gravitate.' The main purpose of the judgment is evidently 



152 Hypothetical and Disjunctive Arguments 

to affirm the necessary connection of the attributes of materi- 
ality and gravitation. The judgment does not refer directly 
to things, or classes of things at all, but asserts without imme- 
diate reference to any particular object, z/ material, //^^/^ gravi- 
tating. The propositions of geometry are still more obviously 
hypothetical in character. 'The three angles of a triangle are 
equal to two right angles,' for example, cannot, without 
violence, be made to mean that the subject is included in the 
class of things which are equal to two right angles. The main 
purpose of the proposition is obviously to assert the necessary 
connection of the 'triangularity' and the equality of angles 
with two right angles, and not to make any direct assertion 
regarding any actually existing object or group of objects. 

We reach, then, the following conclusion: Our thought 
is at once both categorical and hypothetical. As categori- 
cal, it refers directly to objects and their relations. The 
terms of the proposition are then taken in extension to 
represent objects or groups of objects, and the copula to 
assert the inclusion of the subject in the predicate, or, in 
cases of negative propositions, to deny this relation. As 
hypothetical, the reference to things is much more indirect. 
The terms of the proposition are no longer regarded as 
representing objects or classes, but are interpreted from 
the point of view of intension. The judgment affirms or 
denies the connection of the qualities or attributes connoted 
by the terms, and not that of the objects which they denote. 
Sometimes the one aspect of thought, sometimes the other, 
is the more prominent. 

In sense-perception and in simple historical narra- 
tion, assertions are made directly and categorically regard- 
ing things and events. The main interest is in particular 



§ 41- Categorical and Hypothetical Arguments 153 

objects, persons, or events, and our judgments refer directly 
and unambiguously to them. But, as we have already 
seen, our thought from its very beginning attempts to get 
beyond the existence of particular things and events, and to 
discover what qualities of objects are necessarily connected. 
We pass from perception and observation to explanation, 
from the narration of events, to the discovery of the law of 
their connection. And, as a result of this advance, our 
judgments deal no longer exclusively with particular objects 
and events, and the fact of their relation, but with the gen- 
eral laws of the connection between attributes and qualities. 
There is, of course, no fixed point at which we pass from 
the categorical to the hypothetical aspect of thinking. But, 
in general, as we pass from judgments of sense-percep- 
tion and memory, to a statement of theories and laws, 
the hypothetical element comes more and more clearly 
into the foreground. We have seen that it is almost impos- 
sible to interpret propositions regarding geometrical rela- 
tions as referring directly to classes of objects. In the same 
way, it is evident that propositions which state general 
laws are more truly hypothetical than categorical. When 
we assert that ^all men are mortal,' the proposition does 
not intend to state a fact in regard to each and every man, or 
to refer directly to individuals at all, but to express the essen- 
tial and necessary relation between humanity and mortality. 
A proposition which is essentially hypothetical in character 
may then be expressed in categorical form. It must be 
remembered that it is not the form, but the purpose or func- 
tion of a proposition, which determines its character. The 
hypothetical form, however, does justice to an aspect of 
thought which is especially prominent in the universal 



154 Hypothetical and Disjunctive Arguments 

laws and formulas of scientific knowledge, and which is 
not adequately represented by the theory of subsumption, 
or the inclusion of the subject in the predicate. 

§ 42. Disjunctive Arguments. — A disjunctive proposi- 
tion, as we have already seen, is of the form, 'A is either 
B, or C, or D'; a triangle is either right-angled, obtuse- 
angled, or acute-angled. It is sometimes said to be the 
union of a categorical and a hypothetical proposition. On 
the one hand, it asserts categorically regarding A, and with- 
out reference to any external condition. But the disjunctive 
proposition is not simple like the categorical proposition: 
it states its results as a series of related conditions and con- 
sequences. If A is not B, it tells us, it must be either C or 
D; and if it is C, it follows that it cannot be B or D. 

A disjunctive proposition may at first sight appear to be 
a mere statement of ignorance, and, as such, to be less 
useful than the simple categorical judgment of perception. 
And it is true that the disjunctive form may be employed to 
express lack of knowledge. ^ I do not know whether this 
tree is an oak or an ash ' ; 'he will come on Monday or some 
other day.' A true disjunctive proposition, however, is 
not a mere statement of ignorance regarding the presence 
or absence of some fact of perception. It is an attempt, on 
the part of intelligence, to determine the whole series of 
circumstances or conditions within which any fact of percep- 
tion may fall, and to state the conditions in such a way 
that their relations are at once evident. And to do this 
implies positive knowledge. In the first place, the enumera- 
tion of possibilities must be exhaustive, no cases must be 
overlooked, and no circumstances left out of account. Sec- 
ondly, the members of the proposition must be taken so as 



§ 42. Disjimctive Arguments 155 

to be really disjunctive. That is, they must be exclusive of 
one another. We cannot combine disjunctively any terms 
we please, as ' perhaps this ' or ^ perhaps that.' But it is only 
when we understand the systematic connections of things in 
the field in question, that w^e are able to express these con- 
nections in the form, either B or C, and thus assert that the 
presence of one excludes the other. 

A disjunctive proposition, then, presupposes systematic 
knowledge, and is consequently the expression of a com- 
paratively late stage in the evolution of thought. It is 
true that disjunction may involve doubt or ignorance regard- 
ing any particular individual. We may not be able to say 
whether A is B or C or D. But, before we can formulate 
the disjunctive proposition, we must be already acquainted 
with the whole set of possible conditions, and also with the 
relation in which those conditions stand to one another. 
Our knowledge, when capable of being formulated in the 
disjunctive major premise of an argument, is so exhaustive 
and systematic, that the application to a particular case 
effected by the minor premise appears almost as a tautology. 
This will be evident in the disjunctive arguments given below. 

There are two forms of the disjunctive syllogism. The 

first is sometimes called the modus tollendo ponens, or the 

mood which affirms by denying. The minor premise, 

that is, is negative, and the conclusion affirmative. The 

form is, — 

A is either B or C, 

A is not C, 



Therefore A is B. 
The negative disjunctive argument has an affirmative 
minor premise. It is known as the modus ponendo tollens, 



156 Hypothetical and Disjunctive Arguments 

or the form which, by affirming one member of the disjunc 
tive series, denies the others, — 

A is B or C or D, 
But A is B, 



Therefore A is neither C nor D. 



It is, of course, a very simple matter to draw the con- 
clusion from the premises in these cases. As we have 
already indicated, the real intellectual work consists in 
obtaining the premises, especially in discovering the re- 
lations enumerated in the major premise. It is in formu- 
lating the major premise, too, that errors are most likely to 
arise. As already pointed out, it is essential that the dis- 
junctive members shall be exhaustively enumerated, and also 
that they shall exclude one another. But it is not always 
easy to discover all the possibilities of a case, or to formu- 
late them in such a way as to render them really exclusive. 
If we say, ' he is either a knave or a fool,' we omit the possi- 
bility of his being both the one and the other to some extent. 
A great many statements which are expressed in the form of 
disjunctive propositions are not true logical disjunctives. 
Thus we might say, ^ every student works either from love of 
learning, or from love of praise, or for the sake of some 
material reward.' But the disjunction does not answer 
the logical requirements ; for it is possible that two or more 
of these motives may influence his conduct at the same 
time. The disjunctive members are neither exclusive nor 
completely enumerated. 

§ 43. The Dilemma. — A dilemma is, an argument which 
includes all possible assertions about its subject-matter 
under the head of alternatives that involve further con- 



§ 43- T^^ Dilemma 157 

sequences, so that part or all of these consequences must 
be admitted whichever alternative be allowed. In other 
words, ' a dilemma is a compound hypothetical syllogism, 
partly disjunctive in form.' The major premise is always 
hypothetical, and the disjunction is usually stated in the 
minor premise. As the word is used in ordinary life, we 
are said to be in a dilemma whenever there are but two 
courses of action open to us, and when both of these have 
unpleasant consequences. In the same way, the logical 
dilemma when used controversially shuts an opponent in 
to a choice between alternatives, either of which leads to a 
conclusion he would gladly avoid. 

The first form, which is sometimes called the Simple Construc- 
tive Dilemma, yields a simple or categorical conclusion : — 

If A is B, C is D ; and if E is F, C is D, 

But either A is B, or E is F, 



Therefore C is D. 

It will be noticed that the minor premise affirms disjunc- 
tively the antecedents of the two hypothetical propositions 
which form the major premise, and that the conclusion 
follows whichever alternative holds. We may take as a 
concrete example of this type of argument : — 

If a man acts in accordance with his own judgment, he will be 
criticised; and if he is guided by the opinions and rules of others, 
he will be criticised, 

But he must either act in accordance with his own judgment, or 
be guided by the opinions of others. 



Therefore, in any case, he will be criticised. 



158 Hypothetical and Disjunctive Arguments 

The Simple Destructive Dilemma also yields a categorical 
conclusion. But in this form of the dilemma, the major 
premise has one antecedent and two consequents, and these 
consequents are denied in the minor premise. The ante- 
cedent is therefore denied in the conclusion. A famous 
example is the argument of Zeno to show that it is against 
reason to believe that motion really takes place: — 

If a thing moves, it must move either in the place where it is 
or in the place where it is not, 

But it cannot move where it is, nor can it move where it is not, 

Therefore it cannot move^ 

It is worth noticing that in this example the minor premise 
is not disjunctive; that is, it denies the consequents of the 
major premise together^ and not disjunctively. All the 
disjunction here is in the second part of the major premise. 
The Simple Destructive Dilemma is the only form in which 
this occurs, and the disjunction may be in the minor premise 
in this form also. 

The hypothetical propositions which make up the major 
premise of a dilemma do not usually have the same ante- 
cedent or consequent, as is the case in the examples just 
given. When the antecedents and consequents involved 
are different, the dilemma is said to be complex, and the 
conclusion has the form of a disjunctive proposition. In 
the Complex Constructive Dilemma, the minor premise 
affirms disjunctively the antecedents of the major, and the 
conclusion is consequently affirmative. We may take,. as an 
example, the argument by which the Caliph Omar is said 
to have justified the burning of the Alexandrian library: — 

) 



§ 43- ^^^ Dilemma 159 

If these books contain the same doctrines as the Koran, they 
are unnecessary;" and if they are at variance with the Koran, they 
are wicked and pernicious. 

But they must either contain the same doctrines as the Koran 
or be at variance with it, 

Therefore these books are either unnecessary or wicked and 
pernicious. 

A fourth form, the Complex Destructive Dilemma, obtains 
a conclusion made up of two negations disjunctively related, 
by denying disjunctively the consequents of the hypothetical 
propositions that form the major premise of the argument. 
We may take the following example: — 

If an oflQcer does his duty, he will obey orders; and if he is 
intelligent, he will understand them. 

But this officer either disobeyed his orders, or else he misun- 
derstood them, 

Therefore, he either did not do his duty, or else he is not 
intelHgent, 

By taking more than two hypothetical propositions as 
major premise, we may obtain a Trilemma, a Tetralemma, 
or a Polylemma. These forms, however, are used much 
less frequently than the Dilemma. 

The dilemma is essentially a polemical or controversial 
form of argument. Its object, when so used, as we have 
stated, is to force an unwelcome conclusion upon an adver- 
sary by confining him to a choice between two alternatives, 
either of which necessarily leads to such a conclusion. We 
sometimes speak of the horns of the dilemma, and of our 
adversary as ' gored,' whichever horn he may choose. Di- 



i6o Hypothetical and Disjimctive Arguments 

lemmas, however, like all controversial arguments, are more 
often fallacious than valid. The minor premise of a di- 
lemmatic argument, as we have already seen, is a disjunc- 
tive proposition with two members. But it is very rarely 
that two alternatives exhaust all the possible cases. The 
cases enumerated, too, may not exclude each other, or be 
real alternatives at all. The dilemma is thus subject to al 
the dangers which we have already noticed in the case of 
the disjunctive argument. In the minor premise, in addition, 
it is necessary to see that the canon of the hypothetical 
syllogism, ^affirm the antecedent or deny the consequent,' 
is observed. If this rule is not obeyed, the logical form of 
the argument will not be valid. 

A dilemmatic argument may be attacked in three ways, the 
traditional names for which are continuations of the metaphor 
of the ^ horns.' 

(i) One may ^escape between the horns.' This is simply to 
point out that the alternatives presented in the minor premise 
are not exhaustive, and that there are one or more other possi- 
bilities left unmentioned. 

(2) The dilemma may be 'taken by the horns.' That is, one 
may accept the alternative antecedents proposed as exhaustive, 
but deny that one or both of the consequents asserted really follow 
from them. For an example, let us take this argument : — 

If we have trusts, prices will be excessive; and if we do not 
have them, our manufacturing industries will fail to meet foreign 
competition. 

But we must either have trusts or not have them, 

Therefore either prices will be excessive or our manufacturing 
industries will fail to meet foreign competition. 



§ 43- T^^^^ Dilemma i6i 

One might reply to this either by denying that there is any 
inevitable connection between trusts and excessive prices, or by 
denying that trusts are necessary to enable us to compete with 
foreign firms. 

(3) Sometimes, as a reply to a defective dilemma, a counter- 
dilemma is proposed, leading to an exactly opposite conclusion. 
When this is done, the original dilemma is said to be ^rebutted.' 
Whenever such an opposition is possible, each of the two dilemmas 
by itself fails to state exhaustively either the possible antecedents, 
or else the consequents following from the given antecedents. 
Formal rebuttal, therefore, is rather a rhetorical device for showing 
up the weakness of an opponent's position, than a logical argu- 
ment for the direct proof of one's own conclusion. 

A classical example of such rebuttal is the famous Litigiosus. 
Protagoras the sophist is said to have made an agreement to teach 
Euathlus the art of pleading for a fee, one-half of which was to be 
paid to him when he was fully instructed, and the other half when he 
won his first case in court. Euathlus put off beginning his prac- 
tice, and Protagoras finally brought suit for the other half of his fee. 
Protagoras offered the following argument in his own behalf: — 

If Euathlus loses this case, he must pay me, by the judgment of 
the court ; and if he wins it, he must pay me in accordance with the 
terms of his contract. 

But he must either lose it or win it. 



Therefore he must pay me in any case. 

Euathlus then offered the following rebuttal : — 

If I win the case, I ought not to pay, by the judgment of the court ; 
and if I lose it, I ought not to pay, by the terms of the contract, 
But I must either win it or lose it. 

Therefore I ought not to pay. 

The onesidedness of dilemmas which directly confront each other 

M 



1 62 Hypothetical and Disjunctive Arguments 

in this fashion is evident in this example. For a complete statement 
of the case, the major premises of both should be combined. There 
are really two points of view, or standards of reference, involved 
in each alike — the expected judgment of the court, and the terms 
of the contract. Protagoras states the consequent of his first ante- 
cedent in accordance with the first standard, and the consequent 
of the second antecedent in accordance with the second standard. 
Euathlus simply reverses the appHcation of the standards. But 
both disputants make use of the two standards alternately, when one 
only can really be applied. Either the Kteral terms of the contract 
must be observed, and in that case there can be no judgment of the 
court at all, since the proper ground of action — i.e. Euathlus hav- 
ing won his first suit — is not present. The suit must simply be dis- 
missed. Or else, if a judgment in equity is to be granted, and the 
contract interpreted in accordance with its spirit and intention, and 
not with its letter, the appeal is to the judgment of the court on the 
whole case presented, and this judgment will be either for or 
against Euathlus. There is, therefore, no real dilemma involved 
in the circumstances at all, the appearance of it in each argument 
being due to the presence of two contradictory points of view. 

All dilemmas related in this way of direct opposition, using prem- 
ises of the same terms, will be found to involve a similar neglect of 
some aspect of the situation; and this is why we have said that a 
dilemma in rebuttal, while a striking rhetorical device for attacking 
an opponent's position, does nothing to establish the truth of one's 
own. Indeed, if the rebutting dilemma be allowed to remain un- 
supported by any further argument, it may be considered as pre- 
sumptive proof that neither party to the debate has any right to a 
positive conclusion in the matter. Another and simpler example 
may make this clearer: — 

If a man is single, he is unhappy because he has no one to take 
care of him, and if he is married, he is unhappy because he has to 
take care of a wife. (Major premise of original.) 



§ 43- J^^^^ Dilemma 163 

If a man is married, he is happy because he has a wife to take 
care of him ; and if he is single, he is happy because he has no one 
to take care of. (Major premise of rebutting dilemma.) 

Here, as in the former example, the vague and shifting use of 
any standard of reference is apparent in both the original and 
the rebutting dilemma. There is no attempt to define terms, or 
to bring the different standards into relation; the argument 
moves and has its being in the mere limbo of undefined phrases 
where it seems possible to prove anything, just because it is pos- 
sible to prove nothing. 

REFERENCES 

Especially for § 40 

J. S. Mill, Logic, Bk. I,, Ch. V. 
C. Sigwart, Logic, Pt. I., Ch. VII. 

W. Minto, Logic Inductive and Deductive, pp. 129-138, and pp. 
214-225. 

F. H. Bradley, The Principles of Logic, Bk. I., Ch. II. 

B. Bosanquet, The Essentials of Logic, Lecture VI. 

(On § 42) H. W. B. Joseph, An Introduction to Logic, pp. 330-337. 

W. R. Boyce Gibson, The Problem of Logic, pp. 271-277, 292-295. 



CHAPTER XII 

FALLACIES OF DEDUCTIVE REASONING 

§ 44. Classification of Fallacies. — A Fallacy may be 
defined as a conclusion or interpretation, resulting from 
processes of thinking which claim to be valid, but which 
fail to conform to the requirements of logic. Various other 
terms, like ' Sophism/ ' Paralogism/ etc., are employed as 
more or less exact synonyms. We shall hereafter treat of 
the fallacies or errors to which inductive reasoning is most 
subject (Ch. XX.). At present, however, it is necessary to 
consider the fallacies which are likely to attend the employ- 
ment of the syllogistic form of reasoning. In considering 
the subject, we shall find that many fallacies belong equally 
to both kinds of reasoning. This is especially true of errors 
vv^hich arise from the careless use of words. 

The first systematic account of fallacies was given in 
Aristotle's treatise, On Sophistical Difficulties (ire pi aocfyicr- 
TLKOdv iXey^^cop), In this work, Aristotle divides fallacies 
into two classes : those which are due to language (irapa 
rrjv Xe^Lv, or, as they are usually called, fallacies in dictione)^ 
and those which are not connected with language ie^co rrj'^ 
Xe^eco9, extra dictionem). Under the first head, he enu- 
merates six kinds of fallacies, and under the second, seven. 
Aristotle's principle of classification is, however, not entirely 
satisfactory. We must try to find some positive principle 
or principles of classification which will render us more 
assistance in understanding the relations between the vari- 

164 



§ 44' Classification of Fallacies 165 

ous fallacies than is afforded by Aristotle's division into 
those which belong to language, and those which do not. 

In the strict sense of the word, a fallacy is to be defined 
as an error in reasoning. In the syllogism, however, propo- 
sitions or premises form the data or starting-point. If, 
now, these propositions are not properly understood, the 
conclusions to which they lead are likely to be false. We 
may then first divide fallacies into Errors of Interpretation, 
and Fallacies in Reasoning. Errors in interpreting propo- 
sitions might, perhaps, be more properly treated in a work 
on rhetoric than in a chapter on logical fallacies. But it 
has been the custom ever since the time of Aristotle to 
include in the enumeration of logical fallacies a number of 
errors which are likely to arise in interpreting propositions. 
Moreover, as ,we saw in Chapter VII,, there are certain 
processes of interpretation, like Obversion and Conversion, 
which are sometimes called immediate inference, and which 
require a knowledge of the logical structure of proposi- 
tions. 

The Fallacies which arise in the process of reasoning, 
we may again divide into Formal Fallacies, or violations 
of the syllogistic rules, and Material Fallacies. The latter 
class may be further divided into Fallacies of Equivocation 
(including Ambiguous and Shifting Terms, Composition, 
Division, Accident, and the Dilemmatic Fallacy), and Fal- 
lacies of Presumption (including Petitio Principii, Irrele- 
vant Conclusion, Non Sequitur, and Complex Questions). 
The following table will summarize this classification : — 



1 66 



Fallacies of Deductive Reasoning 







Fallacies 

1 


vig 
rial 




Errors in Interpretation 
(i) Illogical Obversion or 




1 
Mistakes in Reasonh 

1 




Conversion 

(2) Amphiboly 

(3) Accent 






1 

Mate 
1 








1 


Formal 




Equivocation 




Presumption 


In Categorical 
Arguments 

T 


(i) Four Terms 

(2) Undistributed 

Middle 

(3) Illicit Major 

(4) Illicit Minor 

(5) Negative 

Premises 

r 


(I) 

(2) 
(3) 
(4) 

(s) 


Ambiguous 
and Shifting 
Terms 

Composition 

Division 

Accident 

Dilemmatic 
Fallacy 


(i) Petitio Prin- 
cipii 

(2) Complex 

Question 

(3) Irrelevant 

Conclusion 

(4) Non Sequitur 


Hypothetical J f\ denying the Antecedent 
Arguments [^7) Affirming the Consequent 






In Disjunctive 1 
Arguments | 


(8) Imperfect Disj 


unction 







§ 45. Errors in Interpretation. — This class of fallacies 
results from iraperfect understanding of the meaning of 
propositions. They are not, then, strictly speaking, errors 
of reasoning at all. If, however, the propositions employed 
as premises in an argument are not correctly understood, 
the conclusions founded upon them are likely to be erroneous. 
And even if the proposition, which is wrongly interpreted, 
is not made the basis of further reasoning, it is in itself the 
result of an intellectual error against which it is possible 
to guard. We do not, of course, profess to point out all 
the possible sources of error in interpreting propositions. 
The only rule applicable to all cases which can be given is 
this: Accept no proposition until you understand its exact 
meaning, and know precisely what it implies. Deliberation 



§ 45- Errors in Interpretatiojt 167 

and attention, both with regard to our own statements 
and those of others, are the only means of escaping errors 
of this kind. 

(i) Illogical Obversion or Conversion. — In a previous 
chapter (Ch. VII.), we have treated of Obversion, Con- 
version, Contraposition, etc., and shown the rules to be 
followed in stating the obverse or the converse of a propo- 
sition. In Obversion, we interpret or show what is involved 
in a proposition, by stating its implications in a proposition 
of the opposite quality. And unless we have clearly grasped 
the meaning of the original proposition, mistakes are likely 
to arise in changing from the affirmative to the negative 
form of statement, or from the negative to the affirmative. 
Thus, we should fall into an error of this kind if we should 
take the proposition, ' honesty is always good policy,' to be 
the equivalent of, or to imply, the statement, ' dishonesty 
is always bad policy.' Nor can we obtain by obversion 
the proposition, ' all citizens are allowed to vote,' from, 
^ no aliens are allowed to vote.' 

In Conversion, we take some proposition, A is B, and 
ask what assertion it implies regarding the predicate. Does 
' all brave men are generous ' imply also that ^ all generous 
men are brave ' ? This is, perhaps, the most frequent 
source of ^ror in the conversion of propositions. I do not 
mean that in working logical examples we are likely to con- 
vert proposition A simply, instead of by limitation. But 
in the heat of debate, or when using propositions without 
proper attention, there is a natural tendency to assume 
that a proposition which makes a universal statement 
regarding the subject does the same with regard to the pred- 
icate. And, although such errors are very obvious when 



1 68 Fallacies of Deductive Reasoning 

pointed out, — as, indeed, is the case with nearly all logical 
fallacies, — they may very easily impose upon us when our 
minds are not fully awake, that is, when attention is not 
active and consciously on guard, or when they occur in 
the midst of a long and complicated argument. Of the 
other methods of interpretation perhaps contraposition is 
most likely to be a source of error. We have already (§ 28) 
given the rules for obtaining the contrapositive of any propo- 
sition. Some practice in working examples will enable one 
to perceive readily what is the logical contrapositive to any 
proposition, and what forms are fallacious. 

(2) Amphiboly^ or amphibology {aii^i^oXia) ^ consists 
in misconception arising from the ambiguous grammatical 
construction of a proposition. A sentence may have two 
opposite meanings, but one may be more natural and prom- 
inent than the other. A deception may be practised by 
leading a person to accept the meaning more strongly sug- 
gested, while the significance intended is the very opposite, 
as, e,g, ' I hope that you the enemy will slay.' In Shake- 
speare's Henry VI, j we have an instance of amphiboly in the 
prophecy of the spirit, that ^^ the Duke yet lives that Henry 
shall depose." Many of the famous utterances of the 
ancient oracles were of this character, as the reported answer 
to Croesus when he inquired at Delphi: ^' If Croesus should 
wage war against the Persians, he would destroy a mighty 
empire." The more ambiguous the oracle, the more read- 
ily it could be explained in accordance with the event, which 
in this case was the destruction of the empire of Croesus. 

(3) The Fallacy of Accent is a misconception due to the 
accent or emphasis being placed upon the wrong words in 
a sentence. It may, therefore, be regarded as a rhetorical 



§ 45- Errors in Interpretation 169 

rather than as a logical fallacy. Jevons's examples of 
this fallacy may be quoted in part. '' A ludicrous instance 
is liable to occur in reading Chapter XIII. of the First Book 
of Kings, verse 27, where it is said of the prophet, ^ And he 
spake to his sons, saying. Saddle me the ass. And they 
saddled him,^ The italics indicate that the word him was 
supplied by the translators of the authorized version, but it 
may suggest a very different meaning. The command- 
ment, ' Thou shalt not bear false witness against thy neigh- 
bour,' may be made by a slight emphasis of the voice on 
the last word to imply that we are at liberty to bear false 
witness against other persons. Mr. De Morgan, who remarks 
this, also points out that the erroneous quoting of an author, 
by unfairly separating a word from its context, or itali- 
cizing words which were not intended to be italicized, gives 
rise to cases of this fallacy." ^ Jevons is also authority for 
the statement that Jeremy Bentham was so much afraid 
of being led astray by this fallacy that he employed a person 
to read to him whose voice and manner of reading were 
particularly monotonous. 

But these misinterpretations of single propositions are 
comparatively trivial instances of this fallacy. In a broader 
sense, the fallacy appears in connected arguments of any 
kind in which, while the facts are not actually misstated, 
certain aspects of them are so disproportionately dwelt, 
upon and emphasized, at the expense of the rest, that a false 
idea of the subject in its entirety is the result. In this 
wider form, this fallacy is one that may be described as the 
particular vice of special pleading; and the caution that 
may be suggested against it is, in the language of the 

^Jevons, Lessons in Logic, p 174. 



1 70 Fallacies of Deductive Reasoning 

astronomer, to make allowances for the ^ personal equation ' 
both in one's own thinking and in that of others. 

§ 46. Formal Fallacies. — We shall follow our table, 
and deal with mistakes of Reasoning under the two head- 
ings of Formal Fallacies, and Material Fallacies. Formal 
fallacies arise from violations of the rules of the syllogism. 
The breaches of these rules have been already pointed out 
and illustrated in our discussion of the various forms of 
syllogistic argument. The analysis of arguments, with a 
view to the detection of such fallacies, where any exist, is 
a very important exercise, and affords valuable mental 
discipline. It seems only necessary here to add a remark 
regarding the first fallacy on our list, that of Four Terms, or 
Quaternio Terminorum, as it is usually called by logicians. 

The first canon of the categorical syllogism states that 
^a syllogism must contain three and only three terms.' 
This rule would of course be violated by such an argument as, 

Frenchmen are Europeans, 
Englishmen are Anglo-Saxons, 



Therefore Englishmen are Europeans. 

It is so obvious that this example does not contain a real 
inference that no one would be likely to be misled by the 
pretence of argument which it contains. In some cases, 
however, a term may be used in two senses, although the 
words by which it is expressed are the same. The following 
example may be given: — 

Every good law should be obeyed, 
The law of gravitation is a good law, 

Therefore the law of gravitation should be obeyed. 



§ 47- Material Fallacies 171 

Here we have really four terms. The word ^ law/ in the 
first proposition, means a command given or enactment 
made by some persons in authority. A ^good law' in this 
sense then means a just law, or one which has beneficial 
results. But in the second proposition it signifies a state- 
ment of the uniform way in which phenomena behave 
under certain conditions. A ^ good law ' from this point of 
view would imply a correct statement of these uniformities. 
It is interesting to note that this example may also be re- 
garded as an instance of Equivocation, and classified as a 
case of an ambiguous middle term. It is often possible 
to classify a fallacy under more than a single head. 

There are, however, cases where an argument may seem 
at first sight to have four terms, but where the defect is 
only verbal. The matter must, of course, be determined by 
reference to the meaning of terms and not merely to the 
verbal form of expression. It is ideas or concepts, and 
not a form of words, which are really operative in reasoning. 
§ 47. Material Fallacies. — What are called material 
fallacies do not result from the violation of any specific 
logical rules. They are usually said to exist, not in the 
orm^ but in the matter of the argument. Consequently, 
it is sometimes argued, the detection and description of 
them do not properly belong to logic at all. We have 
found, however, that all these fallacies have their source 
in Equivocation and Presumption. They thus violate 
two of the fundamental principles of logical argument. 
For all logical reasoning presupposes that the terms em- 
ployed shall be clearly defined, and used throughout the 
argument with a fixed and definite signification. And, 
secondly, logic requires that the conclusion shall not be 



1 72 Fallacies of Deductive Reasoning 

assumed, but derived strictly from the premises. The 
violation of these principles is, therefore, a proper niatter 
of concern to the logician. We shall treat first of the falla- 
cies of Equivocation. 

{A) The fallacies of Equivocation have been enumerated 
as Ambiguous and Shifting Terms, Composition, Division, 
and Accident. These all result from a lack of clearness 
and definiteness in the terms employed. We shall deal 
with them briefly in order. 

(i) The phrase. Ambiguous and Shifting Terms, describes 
the first fallacy of this group. A special case of it appears 
in the Fallacy of Ambiguous Middle, It is obvious that the 
middle term cannot form a proper standard of comparison, 
if its meaning is uncertain or shifting. A standard of meas- 
ure must be fixed and definite. One illustration of this 
case of the fallacy will be sufficient: — 

Partisans are not to be trusted, 
Democrats are partisans, 



Therefore Democrats are not to be trusted. 

The middle term, * partisan,' is evidently used in two senses 
in this argument. In the first premise it signifies persons 
who are personally, or with undue bias, interested in some 
cause ; and in the latter it simply denotes the members of a 
political party. 

But either the Minor or the Major Terms of a syllogism 
may also be ambiguous as well as the Middle, and be used 
in a different sense in the conclusion, than they are in their 
respective premises. One example of ambiguity in the 
Major term may be given: — 



§ 47' Material Fallacies 173 

What is not forbidden by law, no one has a right to prevent my 
doing. 

Reprinting the works of foreign authors is not. forbidden by 
law. 

Therefore, no one has a right to prevent me from reprinting 
such works. 

Here ^ right ' in the major premise means ' legal right ' 
and in the conclusion 'moral right'; ' prevent ' in the major 
premise implies restraint by force or penalty, if necessary, 
but in the conclusion it is used to mean the use of any means 
of restraint whatever. The use of the word ' right ' in 
various meanings is a frequent source of such fallacies, 
and the comment of J. S. Mill on it might well be read by 
the student.^ 

It is often the case, especially where the major or the minor 
term is concerned, that this fallacy cannot be perpetrated 
without some verbal change in the terms, which, however, 
is made plausible by some similarity in theVords employed. 
Aristotle described some of the ways in which such shifts in 
meaning are frequently disguised under the name of the 
Fallacy of Figure of Speech, Words which have the same 
roots may sometimes be substituted one for another, though 
they have taken on different meanings; as, for example, 
the noun ' presumption,' the verb ' presume,' and the adjec- 
tive ' presuming.' Or we may get a wrong meaning for a 
word from its having a similar inflection with other words 
of different meaning. An example of this is the passage 
in which J. S. Mill argues that as what is seen is visible^ and 
v^hat is heard is audible^ so what is desired must be desirable 
"■ Cf. System of Logic, Bk. V., Ch. VII., § i. 



174 Fallacies of Deductive Reasoning 

— therefore morally good. But desirable means primarily 
not what is or can be, but what ought to be desired. 

Then, again, as Archbishop Whately points out, this 
fallacy may be committed by using a term at one time 
in its usual meaning, and at another in its strict etymo- 
logical sense. Thus, he remarks, it is frequently argued 
from the strict original meaning of ^ represent,' that a rep- 
resentative in the legislature is merely the spokesman of his. 
constituents, and has no right to use his independent judg- 
ment in his voting or public utterances. Such reasoning, it is 
obvious, does not necessarily prove anything; for the orig- 
inal meaning of a term may be widely different from the 
true nature and proper functions of the things and per- 
sons to which it later comes to be applied. 

But trivial as such merely verbal argument may seem 
when exposed, it is often a source of confusion. Thus a 
lawyer, for example, might pass from a proper insistence on 
following the original intention and meaning in interpret- 
ing the words of a statute, to the mistaken attempt to deter- 
mine how a new law should be framed by considering what 
the accepted name of the things to which it is to apply meant 
when it was first used. And when an argument is long, 
and is not arranged in syllogistic form, fallacies of this kind 
are much more difficult of detection than in the simple 
examples which have been given. It is of the utmost -im- 
portance, then, to insist on realizing clearly in consciousness 
the ideas for which each term stands, and not to content 
ourselves with following the words. 

(2) The fallacy of Composition arises when we affirm some- 
thing to be true of a whole, which holds true only of one or 
more of its parts when taken separately or distributively. 



§ 47- Material Fallacies 175 

Sometimes the error is due to confusion between the distribu- 
tive and collective signification of ' all/ as in the following 
example: — 

All the a.ngles of a triangle are less than two right angles, 
4, 5, and C are all the angles of this triangle, 

Therefore A^ B, and C are less than two right angles. 

It is, of course, obvious that ' all the angles of a triangle ' 
in the major premise signifies each and every angle when 
taken by itself, and that the same words in the minor prem- 
ise signify all the angles collectively. What is true of all 
the parts taken separately, is not necessarily true of the 
whole. We cannot say that because no one member of a 
Jury is very wise or very fair-minded, the jury as a whole 
are not likely to bring in a just verdict. The members 
may mutually correct and supplement each other, so that 
the finding of the jury as a whole will be much fairer and 
wiser than the judgment of any single individual composing 
it. Another instance of this fallacy which is often quoted 
is that by which protective duties are sometimes supported: — 

The manufacturers of woollens are benefited by the duty on 
woollen goods; the manufacturers of cotton by the duty on cotton; 
the farmer by the duties on wool and grain ; and so on for all the 
other producing classes ; therefore, if all the products of the country 
were protected by an import duty, all the producing classes would 
be benefited thereby. 

But, because each class would be benefited by an import 
tax upon some particular product, it does not necessarily 
follow that the community as a whole would be benefited, 
if all products were thus protected. For, obviously, the 



1/6 Fallacies of Deductive Reasoning 

advantages which any class would obtain might be more 
than offset by the increased price of the things which they 
would have to buy. On the other hand, it would be nec- 
essary to take into consideration the fact that an increase 
in the prosperity of one class indirectly brings profit to all 
the other members of the same society. We cannot regard 
a whole as simply a sum of parts, but must consider also 
the way in which the parts act and react upon one another. 
(3) The fallacy of Division is the converse of Composition. 
It consists in assuming that what is true of the whole is also 
true of the parts taken separately. Some term, which is 
used in the major premise collectively, is employed in a 
distributive sense in the minor premise and conclusion. 
The following example will illustrate this: — 

All the angles of a triangle are equal to two right angles, 
A is an angle of a triangle, 

Therefore A is equal to two right angles. 

To argue that, because some measure benefits the country 
as a whole, it must therefore benefit every section of the coun- 
try, would be another instance of this fallacy. Again, we 
may often find examples of both Division and Composition 
in the practice so common in debate of ' taking to pieces ' 
the arguments by which any theory or proposed course of 
action is justified. A person would be guilty of Division 
if he should argue that, because a complex theory is not 
completely proved, none of the arguments by which it is 
supported have any value. It is, however, perhaps more 
common to fall into the fallacy of Composition in combating 
the arguments of an opponent. Some measure, for example, 
is proposed to which a person finds himself in opposition. 



§ 47' Material Fallacies 177 

It is usually easy to analyze the different arguments which 
have been advanced in support of the measure, and to show 
that no single one of these taken hy itself is sufficient to justify 
the change. The conclusion may then be drawn with a 
fine show of logic that all the reasons advanced have been 
insufficient. This, of course, is to neglect the combined 
effect of the arguments; it is to assume that what is true of 
^ all/ taken distributively, is also true of ' all,' when taken 
in conjunction. And often, as in the case of circumstantial 
evidence, what gives a chain of inference its strength is 
not the particular arguments or facts taken each for itself, 
but what is sometimes called the ' consiliance ' of these 
particulars; that is, the fact that they form a connected 
body of proof all pointing to one conclusion, so that each part 
has a significance, taken in its relation to the whole proof, 
which by itself it would not have. 

But an affirmative form of the fallacy just mentioned is 
also possible in cases where it is attempted to prove the 
possibility or probability of a conclusion by pointing to even 
the high probability, taken separately j of each one of a num- 
ber of conditions which must be true together, in order that 
the conclusion may be true. The mere fact of a large number 
being possible separately may even seem to the careless to 
make the conclusion more probable, when really, if the condi- 
tions must be present together, this becomes less probable 
the more there are of them. What should be proved in such 
cases is of course the probabihty of the conditions as a body; 
and this probability is always less than that of the least 
probable among them taken as occurring by itself. Suppose, 
for example, that we were considering the probability of a 
report being true which had been handed down in succession 

N 



178 Fallacies of Deductive Reasoning 

by A, B, C, and D. What we have to consider is not the 
probabihty of any one of these persons reporting correctly 
by himself, but that of the correct transmission of the report 
through the entire series. Thus, it will be found that if 
the probability of mistake by any one of these persons is 
only I in 5, the probability of error in the final result will be 
approximately 3 in 5. 

(4) It is often difficult to distinguish the various forms 
of the fallacy of Accident from Composition and Division. 
We have seen that the last two rest upon a confusion between 
whole and part; or, as we have already expressed it, on 
an equivocation between the distributive and collective use 
of terms. The fallacies of accident are also due to equivo- 
cation. But, in this case, the confusion is between essential 
properties and accidents, between what is true of a thing 
in its real nature, as expressed by its logical definition, and 
what is true of it only under some peculiar or accidental 
circumstance; or, in other words, a proper distinction is not 
made between the general import of a principle and its appli- 
cation to cases where special modifying conditions are present. 

There are two forms of this argument which are usually 
recognized: {a) The Direct or Simple Fallacy of Accident, 
which consists in arguing that what is true of a thing generally, 
is also true of it under some accidental or peculiar circum- 
stance ; or that a proposition generally true is true in exactly 
the same way when special conditions are present. The 
old logicians expressed this in the formula, a dicta simpliciter 
ad dictum secundum quid. The second form is {b) the Con- 
verse Fallacy of Accident, which consists in arguing that 
what is true of a thing under some condition or accident, 
can be asserted of it simply or in its essential nature; or 



§ 47* Material Fallacies 179 

that a statement which is true when certain conditions are 
present is true generally. The formula for this is, a dicto 
secundum quid ad dictum simpliciter. 

It would be an illustration of the direct fallacy to reason 
that, because man is a rational being, therefore a drunken 
man or an angry man will be guided by reason. Similarly, 
we should commit this fallacy if we were to argue that be- 
cause beefsteak is wholesome food, it would be good for a 
person suffering with fever or dyspepsia; or to conclude 
from the principle that it is right to relieve the suffering of 
others, that we ought to give money to beggars. 

It would be a case of the converse fallacy to argue that 
because spirituous liquors are of value in certain cases of 
disease, they must therefore be beneficial to a person who 
is well. We should also be guilty of the same fallacy, if we 
should conclude that it is right to deceive others, from the 
fact that it is sometimes necessary to keep the truth from a 
person who is sick, or to deceive an enemy in time of war. 

The fallacies of Accident, like all the fallacies of Equivo- 
cation, are largely the result of a loose and careless use of 
language. The source of both forms of the fallacy is one 
and the same. They arise fom the careless use of principles 
or propositions without due regard to the circumstances, 
which determine whether they are properly to be applied, 
unmodified to the case before us. By qualifying our terms 
so as to state the exact circumstances involved, they may 
easily be detected and avoided. 

(5) The Dilemmatic Fallacy arises from the equivocal 
and shifting point of view present in the premises of a di- 
lemma which is open to rebuttal. It has been fully discussed 
at the end of Chapter XL 



i8o Fallacies of Deductive Reasoning 

(B) Fallacies of Presumption, — The fallacies of this 
group are the result of presumption or assumption on the 
part of the person making the argument. It is possible 
(i) to assume the point to be proved, either in the premises 
of an argument, or in a question {Petitio Principii, and 
Complex Question) ; or (2) to assume without warrant that 
a certain conclusion follows from premises which have been 
stated {Non Sequitur) ; or (3) that the conclusion obtained 
is really what is required in order to settle the question at 
issue (Irrelevant Conclusion). 

{a) Petitio Principii, or ' Begging the Question,' is a form 
of argument v/hich assumes the conclusion to be proved. 
This may be done in either of two ways, {a) We may pos- 
tulate the fact which we wish to prove, or its equivalent 
under another name. Thus, for example, we might argue 
that an act is morally wrong because it is opposed to sound 
ethical principles. ' The soul is immortal because it is a 
simple and indecomposable substance,' may be regarded 
as another example of this assumption. A ' question-begging 
epithet ' or cant phrase is often used to bring in such an 
assumption. Thus, Mill remarks, when Cicero discusses 
whether certain propensities, if kept within limits, might 
be regarded as virtuous, he calls them cupiditates, which 
of itself implies that they are vicious. We shall have occa- 
sion to mention this fallacious use of epithets more at length 
when we come to discuss the fallacies of inductive reasoning. 
But (&) the question may be begged by making a general 
assumption covering the particular point in dispute. 
Thus, if the advisability of legislation regulating the hours of 
labour in a mine or factory were under discussion, the ques- 
tion-begging proposition, ' all legislation which interferes 



§ 47- Material Fallacies i8i 

with the right of free contract is bad,' might be propounded 
as a settlement of the whole question. 

A special form of this fallacy results when each of two 
propositions is used in turn to prove the truth of the other. 
This is known as ' reasoning in a circle/ or civ cuius in pro- 
bando. This method of reasoning is often adopted when 
the premise, which has been employed to prove the first 
conclusion, is challenged. ' I should not do this act, because 
it is wrong.' * But how do you know'that the act is wrong ? ' 
* Why, because I know that I should not do it.' 

It is always necessary, then, to see that the conclusion 
has not been assumed in the premises. But, since the 
conclusion always follows from the premises, we may say 
that in one sense the conclusion is always thus assumed. 
It is, therefore, easy to charge an opponent unjustly with 
begging the question. De Morgan, in his work on Falla- 
cies, says: ^' There is an opponent fallacy to the Petitio 
Principii which, I suspect, is of more frequent occurrence: 
it is the habit of many to treat an advanced proposition as 
a begging of the question the moment they see that, if estab- 
lished, it would establish the question." All argument 
must, of course, start from premises to which both parties 
assent. But candour and fairness forbid us to charge an 
opponent with Petitio because the results of his premises 
'are unwelcome. It was Charles Lamb who humorously 
remarked that he would not grant that two and two are 
four until he knew what use was to be made of the admis- 
sion. 

(2) The Complex Question is an interrogative form of 
Petitio, It is not really a simple interrogation, but is founded 
upon an assumption. It tacitly assumes, that is, both 



1 82 Fallacies of Deductive Reasoning 

that certain things are true, and that certain other things 
are false; and therefore any direct answer to it always in- 
volves the admission as true of more than one statement. 
Any discussion or argument whatever, of course, always 
proceeds on the basis of certain assumptions; but there 
should be principles that are accepted as true, at least provi- 
sionally, by all the parties engaged in the discussion, and 
they should be as far as possible made clear and definite 
before discussion begins. In fact, this precaution of mak- 
ing as clear as possible to oneself what one is taking for 
granted is the proper remedy against all the fallacies of pre- 
sumption. Examples of this fallacy may be found in popu- 
lar pleasantries, such as, ' Have you given up your drinking 
habits? ' ^ Do the people in your part of the country still 
carry revolvers? ' Disjunctive questions, too, always contain 
an assumption of this kind: ' Is this an oak or a chestnut? ' 
' Does he live in Boston or New York ? ' The ^ leading 
questions ' which lawyers frequently use in examining wit- 
nesses, but which are always objected to by the opposing 
counsel, are usually of this character. Further instances 
may perhaps be found in the demand for explanation of 
facts which are either false, or not fully substantiated; as, 
e.g, , ^ Why does a fish when dead weigh more than when 
alive ? ' ^ What is the explanation of mind-reading ? ' 

(3) The Irrelevant Conclusion, or Ignoratio Elenchi, con- 
sists in substituting for the conclusion to be proved some 
other proposition more or less nearly related to it. This 
fallacy may be the result of an involuntary confusion on 
the part of the person employing it, or it may be consciously 
adopted as a controversial stratagem to deceive an opponent 
or an audience. When used in this latter way, it is usually 



§ 47' Material Fallacies 183 

intended to conceal the weakness of a position by diverting 
attention from the real point at issue. This is, indeed, a 
favourite device of those who have to support a weak case. 
A counsel for the defence in a law-suit is said to have handed 
to the barrister presenting the case a brief marked, ' No 
case; abuse the plaintiff's attorney.' To answer a charge 
or accusation by declaring that the person bringing the charge 
is guilty of as bad, or even worse, things, — what is some- 
times called the tu quoque form of argument — is also an 
-example of this fallacy. 

Apart from such wilful perversions or confusions, many 
unintentional instances of this fallacy occur. In controver- 
sial writing, it is very natural to assume that a proposition 
which has some points of connection with the conclusion to 
be established, is ^ essentially the same thing,' or ' practically 
the same, as the thesis m^aintained.' Thus one might take 
the fact that a great many people are not regular church- 
goers, as a proof of the proposition that religion and morality 
are dying out in the country. Many of the arguments 
brought against scientific and philosophical theories belong to 
this class. Mill cites the arguments which have been urged 
against the Malthusian doctrine of population, and Berke- 
ley's theory of matter. We may quote the passage refer- 
ring to the former: ^VMalthus has been supposed to be re- 
futed, if it could be shown that in some countries or ages 
population has been nearly stationary, as if he had asserted 
that population always increases in a given ratio, or had not 
expressly declared that it increases only in so far as it is not 
restrained by prudence, or kept down by disease. Or, per- 
haps, a collection of facts is produced to prove that in some 
one country with a dense population the people are better 



184 Fallacies of Deductive Reasoning 

off than they are in another country with a thin one, or 
that the people have become better off and more numerous 
at the same time; as if the assertion were that a dense popu- 
lation could not possibly be well off." ^ Ignorance of the 
methods proper to the subject under discussion is a pro- 
lific source of such fallacies as this. Mere knowledge of 
facts without knowing their meaning is not enough, and 
those whose knowledge is of this description do not see what 
the real questions at issue are, or what constitutes a real 
proof in different subject-matters. As Whately puts it, 
^This is to learn a good many answers without the ques- 
tions.' The history of modern attempts to ^ square the circle' 
furnishes good examples of this ; and scientists of unques- 
tioned authority in their own field are often led astray in 
this way when they attempt to deal, without proper prepa- 
ration, with questions belonging to another science, or to 
philosophy or religion. 

There are several cases or forms of Irrelevant Conclusion 
to which special names have been given, and which it is 
important to consider separately. When an argument 
bears upon the real point at issue, it is called argumentum 
ad rem. But, on the other hand, there are the following 
special ways of obscuring the issue: argumentum ad hom- 
inem, argumentum ad populum, argumentum ad ignorantiam, 
argumentum ad verecundiam^ argumentum ad misericordiam, 
the Fallacy of Objections, and, by extension, the argumentum 
ad baculum. 

The argumentum ad hominem is an appeal to the char- 
acter, principles, or former profession of the person against 
whom it is directed. It has reference to a person or persons, 

1 Logic, Bk. v., Ch. VII., § 3. 



§ 47' Material Fallacies 185 

not to the real matter under discussion. In order to con- 
fuse an opponent, and discredit him with the audience, one 
may show that his character is bad, or that the views which 
he is now maintaining are inconsistent with his former pro- 
fessions and practice. Or, on the defensive side, the char- 
acter of the advocate of the point at issue may be praised. 
Or the argument may be used with the hope of persuading 
the opponent himself. We then try to convince him that 
the position which he maintains is inconsistent with some 
other view which he has previously professed, or with the 
principles of some sect or party which he has approved. 
Or we may appeal to his interests by showing him that the 
action proposed will affect injuriously some cause in which 
he is concerned, or will benefit some rival sect or party. 
In all of these cases the real point at issue is, of course, 
evaded. The only case in which such an argument seems 
at all admissible for the logical purpose of establishing truth, 
and not merely securing conviction, is when the known bad 
character or untrustworthiness of some person is appealed 
to in order to impeach the evidence he may give. Here it 
at least assists us to exclude what is false, and is therefore a 
relevant argument, though one of merely negative character. 
The argumentiim ad populum is an argument addressed to 
the feelings, passions, and prejudices of people rather than 
an unbiassed discussion addressed to the intellect. The use 
of question-begging epithets frequently accompanies this 
fallacy. The argumentum ad misericordiam seems to be only a 
special case of this fallacy, when an appeal is made to the pity 
or sympathy which people may be made to feel for a person 
accused of crime. Or sometimes it may be attempted to rec- 
ommend some party or cause by arousing such feelings for 



1 86 Fallacies of Deductive Reasoning 

its adherents, or a law, by dwelling on the plight of those 
whom it would perhaps relieve. 

The argumentum ad ignorantiam is an attempt to gain sup- 
port for some position by dwelling upon the impossibility of 
proving the opposite. Thus we cannot prove affirmatively 
that spirits do not revisit the earth, or send messages to former 
friends through ^mediums.' Now it is not unusual to find 
ignorance on this subject advanced as a positive ground of 
conviction. The argument seems to be: — 

It is not impossible that this is so, 
What is not impossible is possible, 



Therefore it is possible that this is so. 

The fallacy arises when we confuse what is only abstractly 
possible — i.e. what we cannot prove to be impossible — with 
what is really possible, i.e. with what we have some positive 
grounds for believing in, though these grounds are not suffi- 
cient to produce conviction. 

The argumentum ad verecundiam is an appeal to the rever- 
ence which most people feel for a great name, or for long- 
established usages. This method of reasoning attempts to 
settle a question by referring to the opinion of some acknow- 
ledged authority, without any consideration of the arguments 
which are advanced for or against the position. It is, of course, 
right to attach much importance to the views of great men, and 
to the presumptive evidence of value given by ancient and 
continued use ; but we must not suppose that the opinions of 
the great, or the presumed validity of custom, amount, by 
themselves and unexamined, to final proof, or forbid us to 
consider the matter for ourselves, if we are competent to do so. 

There is, however, a more common, though much less justi- 



§ 47' Material Fallacies 187 

fiable, form of the argument from authority. A man who is 
distinguished for his knowledge and attainments in some par- 
ticular field, is often quoted as an authority upon questions with 
which he has no special acquaintance. The prestige of a great 
name is thus irrelevantly invoked when no significance properly 
attaches to it. Thus, for example, a successful general is 
sometimes supposed to speak with authority upon problems 
of statecraft, and the opinions, of prominent clergymen are 
quoted regarding the latest scientific or political theories. 

The Fallacy of Objections consists, as Whately states it, in 
^' showing that there are objections against some plan, theory, 
or system, and thence inferring that it should be rejected; 
when that which ought to have been proved is, that there are 
more or stronger objections against the receiving than the 
non-receiving of it." This fallacy, he remarks, is ^^ the strong- 
hold of bigoted anti-innovators." In any matter of dispute, 
there will be objections to any solution offered; but this, of 
itself, is no disproof of the conclusion attacked, provided we 
have some positive grounds for it. ^^ There are objections," 
Dr. Johnson once said, ^'against a plenum^ and objections 
against a vacuum; but one of them must be true." 

When all these forms of the fallacy fail, there is still one 
recourse remaining, which takes the matter beyond the bound- 
aries of logic; though, indeed, the other forms are in their 
way quite as irrelevant. This is the argumentum ad haculum, 
which we may translate in current phrase as the ^appeal to 
the big stick.' 

(4) The fallacy of non sequitur, or the Fallacy of the Conse- 
quent, occurs when the conclusion does not really follow from 
the premises by which it is supposed to be supported. The 
following example may serve as an illustration: — 



1 88 Fallacies of Deductive Reasoning 

Pennsylvania contains rich coal and iron mines, 
Pennsylvania has no sea-coast, 

Therefore the battle of Gettysburg was fought in that state. 

This argument, of course, is thoroughly inconsequent, and 
would deceive no one. But when the conclusion repeats some 
words or phrases from the premises, we are likely, when not 
paying close attention, to be imposed upon by the mere form 
of the argument. We notice the premises, and remark that 
the person using the argument advances boldly through ^ there- 
fore' to his conclusion. And if this conclusion appears to be 
related to the premises, and sounds reasonable, the argument 
is likely to be accepted. The following example will illustrate 
this: — 

Every one desires happiness, and virtuous people are happy, 
Therefore every one desires to be virtuous. 

A rather frequent form of this fallacy occurs when we 
think, because we have refuted an argument for a theory, 
that the theory itself is necessarily false, — which would 
be true only if the refuted argument was the only pos- 
sible one for the theory. Or, again, we may think that 
because a conclusion is true, a usual argument for it is 
also true; thus, for example, we might think that because 
God exists, the general consent of all mankind, which used to 
be urged as a proof of His existence, is true. These forms of 
the fallacy may be regarded as simply a breach, within a con- 
tinued argument, of the rules of the hypothetical syllogism 
— ^afRrm the antecedent, or deny the consequent.' For 
in the first form, we argue that because a proof is false, the 
conclusion which would certainly be true if it were true, is 



§ 47- Maternal Fallacies 189 

therefore false; and, in the second, we argue that because a 
conclusion is true, therefore an argument on which it is usually 
made to depend is also true. 

What is known as the False Cause {non causa pro causa; 
post hoc ergo propter hoc) is the inductive fallacy corresponding 
to the non sequitur. In this we assume that one thing is the 
cause of another merely because we have known them to 
happen together a number of times. The causal relation is 
assumed without any analysis or examination, on the ground 
of some chance coincidence. Thus a change in the weather 
may be attributed to the moon, or the prosperity of the country 
to its laws requiring Sunday observance. Or in a case where 
there is really a causal connection we may take the cause for 
the effect, or the effect for the cause. Whately's example of 
this is a good one, because it is a popular fallacy often to be met 
with, especially where the action of natural selection is not 
realized. It is frequently assumed, because the animals and 
men native to countries of inclement climate, where the con- 
ditions of life are severe, are usually robust, that the hardships 
they are forced to undergo in youth are the cause of this 
hardiness; whereas, as a matter of fact, their hardiness was 
the cause of their having survived the hardships. Popular 
notions of hygiene are sometimes largely dependent on this 
confusion. (Cf. § 73.) 

REFERENCES 

J. S. Mill, Logic, Bk. V. 

A. Sidgwick, Fallacies [Int. Scient. Series]. 

R. Whately, Elements of Logic, Bk. III. 



PART II. — INDUCTIVE METHODS 

CHAPTER XIII 

THE PROBLEM OF INDUCTION 

§48. The Problem of Induction. — In Part I. we have 
studied the general nature of the syllogism, and have learned 
what conditions must be fulfilled in order to derive valid 
conclusions from given premises. But the question how the 
premises themselves are established was not discussed. It is 
true that the premises of one syllogism are sometimes proved 
by means of a Prosyllogism, and that it maybe possible to find 
in turn general propositions to support the premises of this 
latter argument. But somewhere this process of formal proof 
must have an end. At last we reach propositions concerning 
which we can say only that their truth is guaranteed by experi- 
ence. It is from experience that propositions are obtained 
like, ^ man is by nature a social being/ ^ water is composed of 
hydrogen and oxygen,' which serve as the premises of syllo- 
gisms. To say that these propositions are learned through ex- 
perience, does not however mean that they have been obtained 
without thinking. For to experience is not merely to feel or 
to have sensations; it is also to put things together, to interpret, 
to appreciate to some extent what our sensations stand for 
and signify. When I say, ^yonder tree is an elm,' this proposi- 
tion is the outcome of my own thinking; it is my interpretation, 

190 



§ 48. The Problem of Induction 191 

on the basis of past experience, of certain sensations of colour 
and light and shade, together, it may be, with certain muscular 
sensations from the movements of the eyes. \ Our thought is 
constantly bringing new sensations and perceptions into 
relation with former experiences, and in this way building 
up and organizing our world of knowledge. To interpret 
the real world — not only the physical w^orld, but the psycho- 
logical and the social world as well — is then the business 
of thought, and this, as we have seen, is to relate the new in 
some way to what we already understand. Our sense percep- 
tions, just as they come, are without order or system. 
Think, for example, of the various things you are sensing at 
the present time. The greater part of these are not consciously 
attended to or thought about; they are taken for granted or 
roughly classified on the basis of some past experience. But 
if one is really thinking, there is some fact or relation that is 
taken as a problem, and for which one is seeking an interpreta- 
tion, i,e, some way of thinking this fact or relation that will 
bring it into place and adjust it to w^hat is already known. 

Apart from this task of interpreting the real world, thought 
has no function, and does not exist. Syllogistic reasoning is 
not a distinct and separate kind of thinking, but is a necessary 
part of the work of building up our knowledge of the world in 
systematic form. Without thinking, then, no knowledge, no 
real experience. But w^e must remember that thinking is no 
mere play of ideas in our heads. It exists only in relation to 
what is objective and real. In a certain sense it always goes 
back to a datum^ to perception. Kant's famous saying that 
^perceptions without conceptions {i.e. thoughts) are blind, 
while conceptions without perceptions are empty,' is well 
worth remembering. 



IQ^ The Problem of Induction 

The problem of Induction ^ with which we are primarily con- 
cerned in this part of the book, is how we are able to derive 
from experience general propositions or principles. It is on 
these, as we have seen, that we base our conclusions in 
syllogistic reasoning. The difficulty is that experience 
seems to give information regarding individual things and 
their qualities only. One learns by experience the qualities 
of this rose, or of this piece of iron; but how is one to dis- 
cover the general nature of the rose or of iron as such ? As 
a matter of fact, we are constantly deriving general statements 
from individual experiences; and in doing this we usually 
bring up, in a more or less systematic way, a number of cases 
or instances and use them as the basis of the general statement. 
And this process of generalization^ or passing to a general 
conclusion on the ground of certain instances or cases that 
have been advanced, may be called Induction {eira^co^rj). 
This definition is, of course, only preliminary, and does not 
attempt to distinguish valid and invalid induction. We have 
to go on to consider more in detail both the conditions neces- 
sary to render the process valid, and the meaning of the gen- 
eralization at which we arrive. 

§ 49. The Enumeration of Instances. — In the first place, 
Induction is not the outcome of a complete enumeration of 
instances; but from an examination of a certain number we 
infer the general mark or principle that is involved in all the 
instances. Where all the instances have been examined, the 
result may be summed up at the end in a proposition that is 
universal in form; but in such a case there has been no Induc- 
tion, no passage to any truth that is really general. For ex- 
ample, after measuring each individual in a company and 
finding that A is less than six feet in height, B less than six 



§ 49- ^^^^ EniiMeration of Instances 1^3 

feet, and so on for the rest, I might make the assertion, ' No 
one in this company is more than six feet tall' This, however, 
would be nothing more than a summation of results, and not a 
genuine Induction at all. Nevertheless, some writers re- 
gard such procedure, where all the instances are examined, as 
the only perfect form of induction. Thus Jevons says: ^^An 
Induction, ... is called Perfect, when all of the possible 
cases or instances to which the conclusion can refer have been 
examined and enumerated in the premises."^ On the other 
hand, where it is impossible to examine all the cases, the induc- 
tive process is regarded as Imperfect by the same writer, and 
the conclusion expressed in the general law as only probable. 
Now this view, though mistaken, is interesting because it 
assumes that it is the business of Induction to count instances. 
When it is possible to examine all the cases we can have cer- 
tainty ; when this is impossible (as is usually true), the unexam- 
ined instances have to be regarded as more or less probable only. 
No other conclusion is possible so long as we merely enumerate 
or cite instances without attempting to analyze them. A 
raere factual connection of two events, P and Q, though ex- 
perienced a thousand times, does not warrant the universal 
proposition, ^All P is Q.' As a matter of fact, scientific In- 
duction always does get beyond a mere citation of unanalyzed 
instances. ^^ Induction which proceeds by merely citing in- 
stances," says Bacon, ''' is a childish affair, and being without 
any certain principle of inference it may be overthrown by a 
contradictory instance. Moreover, it usually draws the 
conclusion from too small a number of instances, taking ac- 
count only of those that are obvious." ^ This is an excellent 

^Elementary Lessons in Logic, pp. 212-213. 

"^ Novum Organum, Bk. I., Aph. CV. "Inductio enim quae procedit 



104 ^'^^ Problem of Inductio7i 

description of the popular unscientific way of seeking to estab 
lish universal connections between events, by citing random 
instances where the events have happened to be found together. 
It is generally easy, for example, to cite instances where dreams 
have come true, or where one member of a dinner party of 
thirteen has died within a year. This species of Induction is, 
as Bacon says, ^''res puerilis,'^^ since it simply asserts the con- 
nection without justifying it or making it intelligible, by bring- 
ing to light any principle of coherency. The possibility of 
contradictory instances is not excluded, and the cases cited 
lack definiteness and precision, no account being taken of the 
attendant circumstances and conditions. 

It should be clear, on reflection, that scientific Induction 
aims at establishing a universal law that does not refer pri- 
marily to cases or instances at all. And the method which it em- 
ploys, as vv^ill be shown later, is to discover the law by analyzing 
the instances and reading it out of them, rather than by merely 
summing them up. When I conclude inductively that 'senti- 
mental people are selfish,' or that 'the maple has a forked fruit- 
key,' the universal statement is not to be taken as merely 
summing up instances. Such propositions are rather asser- 
tions about universal types or kinds — the nature of senti- 
mental people as such, or of maple trees as such. What has 
been established, granting that the induction is valid, is a 
coherence of characters forming a kind or type, so that the 
conclusions might be expressed in hypothetical form: 'if 
sentimental, then selfish,' ' if a maple, then a forked fruit- 
key.' 

per enumerationem simplicem, res puerilis est, et precario concludit, et 
periculo exponitur ab instantia contradictoria, et plerumque secundum 
pauciora quam par est, et ex his tantummodo quae praesto sunt, pronunciat." 



§ 49- ^^^ Enufneration of Instances 195 

To discover such universal principles of connection 
through the analysis and comparison of instances is the goal 
of what may be called Scientific Induction. But we may 
also speak of Enumerative Induction as a lower and less , 
complete form. In practical life we often depend with 
confidence on a conclusion which is based on a somewhat 
careful survey of instances. It is, of course, easier to rest j 
on the authority of the instances, taking the connection as a / 
fact, than to set systematically to work to analyze the in- / 
stances in a scientific way in order to determine exactly the' 
universal form of the law. It is likewise clear that these 
unanalyzed or only partially analyzed instances form the 
starting-point for scientific induction; and that, therefore, 
Enumeration must often play an important part in the pre- 
liminary stages of an investigation. But in certain fields 
of investigation we have to go on counting instances because 
there seems to be nothing else to do. We simply find P 
and Q invariably conjoined as a fact in experience, but are 
unable to analyze out the conditions and so either mediate 
the connection, or exhibit the precise form of the law. We 
cannot get a genuinely universal proposition asserting, ^P 
as such is connected with Q as such,' or, ' if P, then Q.' 
But the i Enumerative conclusion simply afiirms that all i 
instances of P (so far as experienced) are connected with 1 
Q. Nor is the particular nature of the connection defined 
in this form of Induction. P and Q, for example, may be 
connected directly, or in some indirect way, as through a 
common dependence on some third thing, M. In the next 
chapter something further will be said of Enumeration, and 
how it may contribute, when used intelligently, to the ends 
of scientific Induction. Considered in itself, however, as 



196 The Problem of Induction 

dealing merely with instances, we see how far it falls short, 
both in certainty and .exactness, of the ideals of scientific 
knowledge. 

§ 50. Induction through Analysis. — Scientific Induction, 
then, aims at discovering some typical character or law of 
behaviour. This usually requires the examination of a 
considerable number of instances. But the general propo- 
sition is not, however, obtained by simply counting the 
instances, or by adding them together. The purpose of 
taking a number of instances is to facilitate analysis, to aid 
us in eliminating characters or circumstances which are 
accidental or irrelevant, and at the same time, through these 
exclusions, to exhibit and define more clearly the essential 
character and relations of the subject we are investigating. 
The process of analysis is thus at the same time a process 
of synthesis; the process of excluding the irrelevant, a 
process of defining the essential. But it should be noted 
that if the instances are to lead to this result they must, so 
to speak, be selected for this purpose. They are not likely 
to be instructive, if they are chosen at haphazard. If the 
instances were all alike, for example, we should not gain any- 
thing by adding to their number, or if we could discover 
nothing in common among them, we should not be likely to 
select them. It is clear, then, that instances, to be instructive, 
must be selected with reference to the purpose of the inves- 
tigation, and that the work of selecting instances is an essen- 
tial part of the work of induction. It is with this end in view 
that we extend our observations over as wide an area as 
possible, drawing instances from difi'erent parts of the field. 
In natural history, for example, specimens are taken from dif- 
ferent localities, in order to determine by comparison what 



§ 50- Induction through Analysis 197 

features are specific or generic characters, and what mere 
Mocal variations.' What we seek to^obtain is not merely a 
number of instances, but instances which show differences 
that might he significant for our problem. What differences 
or circumstances might be significant, we cannot, of course, 
know in advance. We can only guess, guided by our past 
experience, what might make a difference, and hope, by draw- 
ing instances from different parts of the field, to include all 
the significant circumstances. The function which the 
instances when thus selected fulfil is, of course, to exhibit 
what is essential by eliminating circumstances which are, 
for the purposes of the investigation, superfluous and irrele- 
vant. 

Experimentation, when it is possible, is another way of 
performing the same work of analysis and elimination. 
Hence in fields where experiments can readily be made. 
Induction does not have to depend upon an assemblage of 
instances. The experimenter, having control of the con- 
ditions, can produce the variations he wishes to observe, 
changing one thing at a time and noting the result. In this 
way, he is able to strip the phenomenon of superficial fea- 
tures that are connected with it only accidentally, or in a par- 
ticular case, and by so doing lay bare its universal properties 
and modes of acting. But in experimenting, just as in col- 
lecting instances, there must be a guiding idea or purpose. 
In both cases alike, information is gained only by having 
questions or provisional guesses in mind, and then selecting 
for observation what is necessary to enable us to decide 
which guesses are false and which true. 

What guides the selection of instances in an inductive 
inquiry, and also determines the character of the experiments 



198 The Problem of Induction 

to be performed, is the tentative conception or hypothesis 
which the investigator has in mind. We must look, both 
in collecting instances and in setting up experiments, for 
facts which are significant, that is, which will help to answer 
the questions we have in mind. Bacon discusses at length, 
and classifies under twenty-seven different heads, what he 
calls Prerogative Instances, which, as especially instructive, 
should be the first and last objects of our investigation. 
Some of his headings are: ^ Solitary instances,' ^ migrating 
instances' (where the phenomenon is in process of coming 
into existence or disappearing), ^ clandestine instances,' 
'deviating instances' (as sports, or pathological cases), 
' bordering instances,' and ' crucial instances.' This last 
name {instantia cruets) is drawn from the metaphor of 
the cross erected where two roads meet to indicate the 
different directions. When we have alternative conceptions 
or explanations in mind, either of which appears possible, 
we look for some crucial instance, or devise some crucial 
experiment that will point the way by eliminating one of the 
alternatives.^ To know what facts would really be crucial 
in any given case, it is, of course, necessary to have some 
definite and systematic knowledge of the field in which the 
phenomenon under investigation falls. Only when this 
condition is realized, are we able to interpret rightly the 
bearing of the new instance or experiment on our problem. 
The process of Induction, then, might be represented in 
the form of a Disjunctive Syllogism, where the conclusion 
is reached by eliminating successively all but one of the 
Disjunctive members. For example: — 

^ Examples of crucial experiments may be found among the miscellaneous 
exercises at the end of this volume. 



§ 50. Induction through Analysis 199 

This phenomenon, P, is either A, or B, or C. 

These facts prove that it is not A; and these that it is not B. 
Therefore P must be C. 

This account is fundamentally correct in principle, though 
the Disjunctive Syllogism represents the process as more 
formal than it really is. It is not to be supposed that at 
the beginning of an inductive investigation all the possibil- 
ities are definitely and disjunctively formulated. The va- 
rious possibilities, and their relation to one another, rather 
come to light as the examination and analysis proceed. 
And, at the end, the conclusion is never merely the result 
of the process of exclusion. In other words, we do not accept 
C merely because we cannot think of anything else; but, 
through the process of excluding A and B, C has become, 
to some extent at least, positively defined and determined. 
In dealing with any real problem, we cannot make any 
significant denial without thereby implicitly affirming and 
defining something else. These considerations will come 
up for discussion again, particularly in Chapter XVIII. , 
where an account is given of the more explicit use and nature 
of hypotheses. In the meantime, however, the disjunctive 
principle may be regarded as the working basis of inductive 
procedure, though, especially in the earlier stages of this 
process, the disjunctive members are not formally enumer- 
ated, or set over against one another as exclusive possibilities. 

Where now, we may ask, do the conceptions which are 
thus put forward in more or less definitely disjunctive form, 
and tested by means of instances and experiments, have 
their source ? They arise in the mind itself, and are expres- 
sions of its own theorizing activity. These conceptions, 
however, are not mere uninstructed guesses, but are for- 



200 The Problem of Induction 

mulated in the light of the knowledge already achieved. In- 
duction, as a scientific process, bases itself on the relations 
and distinctions that are found in ordinary experience, and 
simply carries these farther and makes them more definite 
and consistent. Now, in the language of ordinary life, there 
is already given a preliminary classification and arrangement 
of the fundamental aspects of experience. In ordinary 
speech and in everyday practical relations, there is present 
a certain organization of experience. And it is this which 
is taken as the starting-point for the scientific interpreta- 
tions which are to correct and extend the old. The phe- 
nomenon that we set out to interpret can only be under- 
stood in the light and with the help of what is already 
assumed as known. It is because we are able to perceive 
or imagine the likeness of the new to something with which 
we are already familiar that it is possible to think it in 
relation to the rest of our experience. If any phenomenon 
were to appear as absolutely unclassifiable, or totally un- 
like anything ever experienced before, there would be no 
means of getting hold of it, so to speak. And just because 
it might be anything, it would be for us as good as nothing. 
Even to attend to it would be impossible, for attention in- 
volves comparison. But the truth is that new facts and 
experiences always appear as modifications or variations of 
existing experience. In other words, although they have the 
element of unfamiliarity, it is yet always possible to discover 
in them some point of resemblance or identity with what 
has gone before. This resemblance or analogy in certain 
respects with what is already familiar leads us to assume that 
they may be of the same general type or kind as the latter, 
and that they will be found to have similar properties or 



§ 50. Induction through Analysis 20 1 

modes of operation. But this is as yet only an assumption 
that must be tested before being accepted as true. Further 
analysis may show that this assumption is based on a mere 
surface resemblance which does not warrant the interpre- 
tation made. Or, as is more usually the case, examination 
may disclose analogies which only allow the phenomenon to 
be classified as belonging to this or that general field. But 
the point to be noted is that through analogy its sphere has 
been determined. There are now only a definite number 
of possible interpretations, which take more or less definitely 
the form of a disjunctive proposition; P falls in the general 
field M, and is, therefore, A or B or C. Each member is put 
forward on some positive ground, and is thus a genuine 
possibility, not a mere unsupported guess. But it is only a 
possibility — something whose truth is still to be deter- 
mined — and so its function is to operate as a plan or schema, 
pointing the way to further examination and testing through 
new instances and observations. 

Our discussion has accordingly shown that Induction 
is able to pass from instances to a general conclusion only 
when the instances are selected because of their bearing 
on conceptions and hypotheses with which we are experi- 
menting. Moreover, in forming these tentative hypotheses, 
we are guided in the first place by the analogy of the phenome- 
non under investigation to what is already known. Analogy 
and Hypotheses are then indispensable in Induction from 
the beginning, though the account of the more formal and 
explicit use of these operations is postponed to the later 
chapters. 



CHAPTER XIV 

THE ASSUMPTIONS OF INDUCTION — STAGES IN THE INDUC- 
TIVE PROCEDURE 

§ 51. The Assumptions of Induction. — It is part of the 
task of Logic to make us conscious of the assumptions of 
our thinking. We have found, in deahng with syllogisms, 
that it is often necessary to look for the premise or principle 
assumed in drawing the conclusion. But, in addition to 
these special assumptions which are taken as the basis of 
argument in particular cases, there are more general assump- 
tions made by each science in the very process of defining 
its own standpoint and working conceptions (cf, § 95). 
Moreover, still more general assumptions may characterize 
groups of sciences, as, for example, the natural sciences, 
the historical sciences, etc. Finally, the question may be 
raised as to what is assumed in all thinking — what are the 
universal assumptions of thought — and what form these 
assumptions take in Induction. In § 9 we spoke of the 
Laws of Thought, and under the name of Identity and Con- 
tradiction, reference was made to the principles of consistency 
on which syllogistic logic is based. Now since Induction 
and Syllogism, as both processes of reasoning, are different 
rather in form than in fundamental character, their assump- 
tions are not unrelated to each other. Indeed, the assump- 
tions of Inductive thinking are more concrete expressions 

of the laws of thought than are the formal expressions of 

202 



§ 51. The Assicmptions of Induction 203 

Identity and Contradiction, mentioned in connection with 
the syllogism. 

What we appear to assume in inductive reasoning is that 
the reahty with which thinking is deahng is systematic and 
coherent. There is no direct method of proving that the 
w^orld is not composed of a collection of particular things 
resembling one another more or less in an accidental or exter- 
nal way, but at bottom having nothing to do with one another. 
The only proof is that it would be impossible either to under- 
stand or to deal practically with such a world. For it would 
be a world in which experience could teach us nothing, since 
events might happen in any order or in any way, and it 
would never be possible to infer anything. We assume, there- 
fore, and must assume, that the world is a cosmos, not a chaos. 
And this means that there are universal relations and con- 
nections of events which, if once discovered in their true 
nature, may always be depended upon. ^ What is once true 
is always true.' A (e.g. the properties of iron, or the prin- 
ciples of heredity), once accurately determined and defined, 
is A, however various may be the instances in which it ap- 
pears. To say, as is sometimes done, that in Induction 
it is assumed that what is true of certain instances will be 
true of all other instances w^hich resemble these, is not en- 
tirely accurate. For, as we have seen, genuine induction 
is not based on instances at all, but on the discovery through 
analysis of a typical nature or law of action. What our 
thinking assumes is that identity of law and identity of nature 
exist in and through the diversity of things, and that it is in 
virtue of these universal principles of connection that the world 
is a coherent and intelligible system. Induction is only 
possible on the assumption that things not only are together 



204 ^'^^ Assumptions of Induction 

but helong together. On this assumption it has to work 
out the special mode of ^belonging' in various fields of phe- 
nomena; to bring to light the identity of nature or law 
that connects things which at^ first sight appear diverse and 
unrelated. 

(i) The question of how this identity of nature, which connects 
things, is to be conceived, is a very fundamental one, both in science 
and philosophy. We have already seen that, to discover a genuine 
identity, it is necessary to penetrate beyond striking resemblances 
and superficial sense qualities to some deeper-lying nature. More- 
over, the universal nature of a thing cannot be discovered in the 
form of some essence or substance that remains permanent and 
unchanging. It must rather be conceived dynamically, as a mode 
of activity, or rather as a system of activities in which all the parts 
are involved, and through which they are correlated. And, fur- 
thermore, the activity of a thing, which constitutes its nature, 
carries it, so to speak, beyond its own boundaries. It acts 
upon other things, and is in turn influenced by them. Its so- 
called properties are statements of its relation to other things. 
It cannot, therefore, be conceived as an isolated, unchanging 
essence, but must be defined through the constancy of behaviour 
shown in its changing relations to its environments. For exam- 
ple, the universal nature of man is not found in some unchanging 
substance, either material or spiritual, that inheres in the different 
human individuals. It consists rather in the system of functions, 
physical and mental, through which he expresses his relation to 
the world of persons and things. Nor, in the case of man, are 
the activities which constitute his nature modes of reacting with 
unvaried uniformity, but functions of adjustment and organiza- 
tion which develop in the light of the work they are called upon 
to perform. 

(2) The particular forms of relation which are employed by 



§ 52. Stages in the Inductive Process 205 

our thought to connect things are known as Categories. Thus in 
the last paragraph, we have been insisting that things are to be inter- 
preted by means of dynamical rather than static categories. Simi- 
larly we might speak of Cause and Effect, or Energy, or Unity of 
Plan (Purposiveness) , as Categories, since they are different forms 
or conceptions which we employ in thinking things in relation. 
Now each group of sciences has its own standpoint and categories, 
its own special terms in which it describes things and their relations. 
Thus physics represents the phenomena with which it deals, as 
mechanically or externally determining one another as causes and 
effects, while biology explains the actions of living organisms 
largely in terms of adjustment and purpose. What particular 
categories are employed by any science depends partly on the 
nature of the facts, and partly on the purpose which the science 
has in view. 

(3) If the Maw of thought' or ^inductive assumption' be true, 
all the various parts of the world must ultimately be related 
through some law, or system of laws. So much seems to be implied 
in the very conception of a ^universe.' To find some terms in 
which a universe can be thought is the task of philosophy. What, 
then, is to be the highest or ultimate category of philosophy ? To 
what common conception may all the diverse and seemingly 
irreconcilable phases of the world be reduced ? The two oppos- 
ing forms of answer given by philosophy to these questions are: 
(i) the common basis of all things consists in some form of matter 
or physical energy (Materialism) ; (2) the unity of the world is to 
be conceived in terms of an idea, or inner purposiveness, through 
which all the parts and functions find their explanation (Idealism), 

§ 52. Stages in the Inductive Process. — Induction we 
have already seen to be a process of interpreting facts in 
terms of general conceptions or principles. This description 
would, however, apply equally w^ell to Deduction; and, as a 



2o6 The Assumptions of Induction 

matter of fact, these are not different kinds of thinking, but 
different methods^ which are necessary to supplement each 
other in the task of making things intelhgible. [ The various 
sciences have to start with particular facts learned through 
experience. The knowledge of general laws and principles 
comes later, and is derived from a study of the particular facts, j 
It is clear, then, that the procedure of all the sciences must be 
inductive, at least in the beginning. The various sciences are 
occupied, each in its particular field, in the task of discovering 
order and relation among phenomena that at first sight appear 
to be lawless and disconnected. But in carrying out this 
undertaking our thinking uses every means which will help it 
toward its desired end. It is often able, after pushing induc- 
tive inquiries a little way, to discover some general principle, 
or to guess what the law of connection must be. When this 
is possible, it is found profitable to proceed deductively, 
reasoning out what consequences necessarily follow from the 
assumption of such a general law. Of course, it is essential 
to verify results obtained in this deductive way by compar- 
ing them with facts as actually experienced. The truth is 
that it is impossible, in actual thinking, to separate induction 
and deduction: the two processes constantly go hand in hand 
and are mutually supplementary. 

Again, it must be remembered that the inductive process, 
considered broadly as the progressive interpretation of expe- 
rience, is continuous throughout. AVhat is already known is 
always taken as the starting-point for a new investigation. 
And although the imm^ediate purpose of any special inquiry 
may soon be satisfied, the results obtained lead to new ques- 
tions, which can be answered only by further analysis and 
investigation. There is then no break — no fundamental sep- 



§ 53- Observation and Explanation 207 

aration — between the facts with which induction starts and 
the more highly developed theories and generahzations which 
it is sometimes able to reach. What we call facts are them- 
selves the results of former processes of thinking and inter- 
pretation, as well as the starting-point for new analysis and 
theorizing. There is a constant passage from one stage to the 
other, theories when approved and generally accepted coming to 
be regarded as facts, and facts when critically examined disclos- 
ing the theoretical basis on which they rest. For example, we 
say that it is a ^ fact ' that the earth revolves on its own axis. 
Yet this, not very long ago, was regarded as an ' incredible 
hypothesis.' And when we reflect, we see that this ^ fact ' is 
really a conception — or a part of a system of conceptions — 
which enables us to bring together in our thought a number of 
simpler ^ facts.' And these latter, if examined, would in turn 
prove to be constructed by coordinating and generalizing 
still simpler data, the truth being that all facts involve ideas. 

Whew ell has spoken of Induction as "^ the true colligation of 
facts by means of an exact and appropriate conception"; and 
he goes on to point out that the distinction of fact and theory 
is only relative. "' Events and phenomena considered as par- 
ticulars which may be colligated by Induction, are facts; 
considered as generalizations already obtained by colligation 
of other facts, they are theories." ^ 

§ 53. Observation and Explanation. — The Inductive pro- 
cess being thus continuous, how are its different sta^ges to 
be distinguished and classified? We may still adopt the 
customary terms, and speak of Induction as including both 
Observation, or Description, and Explanation, though it must 
be remembered that the one process really involves the other. 
^ 'Novum Organon Renovatum, Bk. II., Aph. XXIII. 



2o8 The Assumptions of Induction 

Sometimes the relation between Observation and Explana- 
tion is stated in quite a misleading way. It is said that in 
undertaking an investigation we must observe and describe 
the facts as accurately as possible, and only after this is done 
proceed to theories and explanations. Now, as has been 
shown, this is to make an artificial separation between col- 
lecting and describing the facts, and relating or explaining 
them. As we have seen, both processes go on simultaneously. 
The observation of instances presupposes some guiding idea, 
some provisional hypothesis, perhaps held in the mind as a 
question to be answered. We discover the relevant facts as 
we go along with our investigation, just as we discover the 
appropriate conception or explanation. And just as the facts 
observed and described involve theories and conceptions, so 
the explanation to which we proceed is simply a fuller and 
more accurate description. When the close and necessary 
relation of these stages of Induction is kept in mind, there is, 
however, some advantage in maintaining the distinction be- 
tween Observation of the nature of particular facts and the 
wider organization of facts and relations effected by what 
we call Explanation. 

It is the business of the former process to employ various 
methods and devices in order to determine as accurately as 
possible the nature of the starting-point. It is essential to have 
a full and accurate survey of the terms of the problem, and 
to note carefully every clew that may lead to its solution. In 
the first place, the different qualities of things must be accu- 
rately observed and distinguished. But accurate observation 
in science leads almost directly to the determination of quan- 
titative relations through measurement. Under this head fall 
processes of enumeration, the measurement and recording 



§ 53- Observation and Explanation 209 

of space and time relations, the determination of weights, 
and the measurement of the so-called secondary quahties like 
heat, sound, and colour. The special technique through which 
such observations are carried out and rendered precise in 
the different sciences, must be learned through occupation 
with the actual phenomena. In each science, questions arise 
regarding methods of measurement — the determination of 
the units to be employed, means of measuring indirectly when 
direct measurement is impossible, the most accurate method of 
summing up observations and of eliminating errors — as well 
as problems regarding the most convenient means of represent- 
ing quantitative relations through mathematical formulae, 
graphs, etc. In addition, the use and manipulation of various 
instruments designed to supplement and render more accu- 
rate the observations of the senses have to be learned; the 
fingers often require to be trained to perform delicate opera- 
tions ; and a special education of the senses and attention is 
necessary in some fields before results of scientific value can 
be obtained. This technical knowledge and skill in the 
employment of the instruments and methods of observation 
and description within any science is to be attained, as already 
stated, only by actual practice. We distinguish practically 
this work of collecting data — which may be extended over 
months or years — from the construction of the explanatory 
theory, the former often seeming to demand the power of 
patient observation and skill in mechanical manipulation 
rather than logical reasoning. 

It is important, however, to remember that scientific 
observation itself involves intellectual activity. To observe — 
at least in the sense in which the word is used in scientific pro- 
cedure — requires something more than the passive reception 



210 The Assumptions of Induction 

of impressions of sense in the order in which they come to 
us. Without some activity on the part of mind, it would be 
impossible to obtain even the imperfect and fragmentary 
knowledge of everyday life. But accurate observation is one 
of the means w^hich science employs to render this know- 
ledge more complete and satisfactory; and when observation 
thus becomes an exact and conscious instrument, it involves, 
to even a greater extent than in ordinary life, inteFectual 
activities like judgment and inference. It is because this is 
true, because scientific observation demands the constant 
exercise of thought, in selecting and comparing the various 
elements in the material with which it deals, that it affords 
such excellent intellectual discipline. The observational 
sciences do not merely train the sense-organs; the discipline 
which they afford is mental as well as physiological, and it 
is, of course, true that mental training can only be gained 
through the exercise of mental activity. 

(i) It is quite true that it is of the utmost importance to 
distinguish between a fact, and further inferences from the fact. 
As will be pointed out in the chapter on Inductive Fallacies, 
errors very frequently arise from confusing facts and inferences. 
This does not mean, as we have seen, that facts exist apart from 
theories. But in any particular case if we would avoid confusion, 
we must distinguish sharply between the data and further con- 
structions to which we proceed. Especially important is it not to 
confuse facts with fancies, or with judgments motived by subjec- 
tive feelings. The point which is emphasized in the previous 
paragraph, however, is that it requires a certain amount of think- 
ing in order to get a fact at all. Facts do not pass over ready- 
made into the mind. Simply to stare at things does not give 
us knowledge: unless our mind reacts, judges, thinks, we are 



§ 53. Observation and Explanation 21 1 

not a bit the wiser for staring. To observe well, it is neces- 
sary to be more or less definitely conscious of what one is looking 
for, to direct one's attention toward some particular field or object; 
and to do this implies selection among the multitude of impressions 
and objects of which we are conscious. Moreover, scientific obser- 
vation requires analysis and discrimination. It is not unusual, in 
text-books on logic, to symbolize the various facts learned through 
observation by means of letters, a, &, c, etc., and to take it for granted 
that they are given in our experience as distinct and separate phe- 
nomena; but, as we have just seen, judgments of analysis and 
discrimination are necessary to separate out the so-called ^phenom- 
ena' from the mass or tangle of experience in which they were 
originally given. Again, to determine the nature of a fact through 
observation, it is essential to note carefully how it differs from 
other facts with which it is likely to be confused, and also, to some 
extent, what relations and resemblances it has. But such know- 
ledge presupposes that thought has already been at work in forming 
judgments of comparison. 

(2) A distinction is sometimes made between observation 
and experiment. In observation, it is said, the mind simply ^;z^5 
its results presented to it in nature, while in experiment the answer 
to a question is obtained by actively controlling and arranging the 
circumstances at will. There are, no doubt, some grounds for 
this distinction, though it is not true that the mind is passive in the 
one case, and active in the other. Even in observation, as we have 
seen, knowledge always arises through active analysis and compari- 
son of the instances selected as having a bearing on some problem. 
The difference is rather this : In observing, where experiment is im- 
possible, one must wait for events to occur, and must take them in 
the form in which they are presented in the natural order of events. 
ButjWhere experiment is employed, we have control of the conditions, 
and can produce the phenomena to be investigated in any order, and 
as often as we choose. In experiment, as Bacon says, we can put 



212 The Assumptions of Induction 

definite questions to nature, and compel her to answer. This is, 
of course, an immense advantage. In some of the sciences, how- 
ever — geology and astronomy, for example — it is not possible 
directly to control the conditions : one must wait and observe the 
results of nature's experiments. Physics and chemistry are the 
experimental sciences par excellence; and, in general, we may say 
that a science always makes more rapid progress when it is found 
possible to call experiment to the aid of observation. It is not 
possible to conceive how physics and chemistry could have reached 
theirpresent state of perfection without the assistance of experiment. 
And the rapid advances made in recent years by biology and psy- 
chology have come mainly through the introduction of experimental 
methods. Indeed, the almost total neglect of experiment by the 
Greek and mediaeval scholars must be regarded as one of the chief 
reasons why the physical sciences made so little progress during 
those centuries. 

We have seen that the distinction between observation and 
explanation is not an absolute one. The task which thought 
has to perform — the task w^hich is undertaken by science — 
is to reduce the isolated and chaotic experiences of ordinary life 
to order and system. And it is important to remember that 
all the various methods employed contribute directly towards 
this result. It has, however, seemed possible to divide Induc- 
tive methods into two main divisions. Observation, it was 
said, seeks to discover the exact nature of the facts to be dealt 
with, and to find accurate means of describing and represent- 
ing their qualitative and quantitative aspects. But, when this 
has been accomplished, we have not by any means reached 
an end of the matter. The desire for knowledge is not satisfied 
with a mere statement of facts, or even with a mathematical 
representation of them in a formula or a curve. Complete 



§ 53- Observation and Explanation 213 

knowledge demands an explanation of the facts as determined 
by the methods of observation. The scientist is not content 
to know merely that such and such phenomena happen in cer- 
tain definite ways, but he attempts to discover why this is so. 
^ Why/ we ask, ^ should dew be deposited at certain times, or 
water rise thirty-two feet in a pump ? ' The demand is that 
the processes of analysis be pushed farther by thought. What 
is required is a wider generalization, or the discovery of a more 
general law of behaviour under which the phenomenon we 
are studying may fall as a special case. Yet this explanation, 
when arrived at, is on one side nothing more than a more com- 
plete description of the facts, calling attention to forces and 
happenings that escape ordinary observation. The expla- 
nation of the pump, for example, called attention to the weight 
of the atmosphere, hitherto neglected. But the new inductive 
step consists in something more than the addition of new facts. 
What is essential in explanation is rather the new way of col- 
ligating or thinking the facts in relation to one another, 
afforded by the law or conception. The difference between 
Description and Explanation is obviously one of degree, being 
simply a question of how far analysis is pushed. In general, 
we speak of a conception as explanatory rather than descrip- 
tive, when it explicitly brings different facts into relation. 
Of course. Explanation itself has various degrees of complete- 
ness and ultimateness. There always exists the ideal of a 
higher generalization, a more complete colligation of facts 
than any which science and philosophy have yet been able to 
achieve. 

An excellent illustration of the distinction between descrip- 
tive and explanatory conceptions is afforded by a comparison 
of the work of Kepler with that of Newton. Kepler was filled 



214 The Assumptions of Induction 

with the idea that there must be some relation capable of math- 
ematical expression between the different positions, previously 
determined by observation, in the orbit of the planet Mars. 
At length, after trying and discarding numerous other hy- 
potheses, he was able to show that an ellipse could be passed 
through all these points. The proof was afterwards worked 
out of the elliptical character of the orbits of the other planets. 
The conception of an ellipse enabled Kepler to think all the 
observed positions of the planets, in relation to one another. 
But the explanation of why the planets moved through ellip- 
tical orbits was still lacking. That explanation, as is well 
known, was given by Newton in his conception of universal 
gravitation. This was explanatory because it linked together 
the movements of the planets with the behaviour of all other 
bodies moving in space, thus enabling the former to be 
thought as examples or instances of the action of a universal 
principle. -^^ 

It is usually said that where we know merely the nature of phe- 
nomena, and their connection, without being able to explain these 
facts, our knowledge is empirical. Thus, I may know that an ex- 
plosion follows the contact of a lighted match with gunpowder, or 
that a storm follows when there is a circle around the moon, without 
being able to explain in any way why these facts are connected. 
On the other hand, if we can connect events by showing the gen- 
eral principle involved, we say that our knowledge is really scientific. 
It is important to notice, however, that empirical knowledge is simply 
in a less advanced stage than the scientific knowledge which has suc- 
ceeded in gaining an insight into the general law; and also that 
any knowledge might be called empirical, when contrasted with a 
more complete explanation. Thus Kepler's knowledge, that the 
orbits of the planets are ellipses, was empirical compared with that 



§ 53- Observation and Explanation 215 

of Newton. Empirical knowledge leaves a problem which intelli- 
gence has still to solve. It is, of course, true that a large part of 
every one's knowledge is empirical in character. We all know 
many things which we cannot explain. In all the sciences, too, 
phenomena are met with which seem to defy all attempts at expla- 
nation. Indeed, some of the sciences can scarcely be said to have 
passed the empirical stage. The science of medicine, for example, 
has hardly yet reached any knowledge of general principles. The 
physician knows, that is, as a result of actual experiment, that 
such and such drugs produce such and such effects. But he 
knows almost nothing of the means by which this result is achieved, 
and is therefore unable to go beyond the fact itself. In this respect, 
he is very little better off than the ordinary man, who knows that 
if he eats certain kinds of food he will be ill, or if he drinks strong 
liquors in excess he will become intoxicated. 

REFERENCES TO CHAPTERS XIII AND XIV 

C. Sigwart, Logic, Vol. II., Ch. V. 
B. Bosanquet, Logic, Vol. II. ^ Chs. II.-V. 

H. W. B. Joseph, An Introduction to Logic, Chs. XVIII. and XIX. 
W. Whewell, Novum Organon Renovatum. 
L. H. Hobhouse, The Theory of Knowledge, Chs. XI.-XIV. 
W. P. Montague, " On the Nature of Induction,'' Journal of Philos. 
and Psych.y Vol. III., pp. 281 ff. 



u 

CHAPTER XV 

ENUMERATION AND STATISTICS 

§ 54. Enumeration or Simple Counting. — We shall begin 
the account of the scientific methods with Enumeration. To 
count the objects which we observe, and to distinguish and num- 
ber their parts, is one of the first and most essential operations 
of thought. It is of course true that qualitative distinctions 
generally precede quantitative. The child learns to distin- 
guish things by some qualitative mark, such as ^ black' or 
^hot,' before he is able to count them (cf. § 87). We may 
say, however, that the qualities of things are known, in a 
general way at least, before scientific procedure begins. The 
determination of quantity, on the other hand, seems to 
demand a more conscious effort on the part of the mind. We 
learn to distinguish the general qualities of things without 
effort; but, in order to obtain quantitative knowledge, it is 
necessary to set ourselves deliberately to work. And it is also 
necessary, as we shall see, to decide what we shall count. We 
must make up our mind, with some general idea more or less 
consciously before us, what it is worth while to enumerate. 
We may, accordingly, take Enumeration, or Simple Count- 
ing, which is perhaps the easiest kind of quantitative 
determination, as our starting-point in dealing with the 
Inductive Methods. 

A considerable step in advance, in the task of reducing the 

216 



§ 54- Enumeration or Simple Counting 217 

world of our experience to order and unity, is taken when we 
begin to count, i.e. to group together things of the same kind, 
and to register their number. Thus Enumeration is, to some 
extent, also a process of classification. What is counted is 
always a collective whole, the units of which are either all of 
the same kind, or else belong to a limited number of differ- 
ent classes. Thus one might determine by Enumeration the 
number of sheep in a flock, taking each individual as belonging 
to the same general class, ^ sheep '; or the analysis might be 
pushed farther so as to give as a result the number of white and 
of black sheep separately. The purpose for which the enu- 
meration is undertaken always determines the length to which 
the process of analysis and distinction is carried . For example, 
if the object of a census enumeration were simply to determine 
the number of inhabitants in a country, it would not be neces- 
sary to make any distinctions, but each person would count as 
one. But where, as is often the case, the aim is not simply to 
count the sum-total, but also to determine the relative numbers 
belonging to various classes, analysis has to be pushed further. 
In such cases, we might count the number belonging to each 
sex, the native-born, and those of foreign birth, those below, 
and those above any given age, etc. 

In the last chapter we have seen that the so-called ^ Perfect 
Induction,' where all instances are examined, is not properly 
called Induction at all, since there is no inference to anything 
new. Scientific Induction analyzes, notes special accompany- 
ing circumstances, and gets beneath the surface to the real or 
essential happening in the various cases. But we saw that 
before the process of analysis is carried out, as well as in cases 
where the conditions are too complex or difficult to determine, 
we do proceed to generalize with greater or less confidence on 



2i8 Enumeration and Statistics 

the basis of the instances observed. If instances of P and Q, 
for example, have always been found in conjunction, and if vs^e 
are confident that there has been nothing limiting or restrict- 
ing observation to some special type of instance, we assume 
that the connection is not a mere ' casual coincidence,' but 
that in some form it holds universally. In such cases, the 
number of instances — provided they can he assumed to he 
really unrestricted — does seem to have a bearing on the logical 
character of the conclusion. The connection P — Q is less 
likely to be merely ^casual' in proportion to the frequency 
with which ^ free, or unrestricted ' cases of it are observed, while 
at the same time no exceptions to it appear. The ^ imperfect ' 
character of the Induction, when based on a number of care- 
fully established instances that show no exception throughout 
a considerable range, is found rather in the fact that thenature 
of the connection P — Q is left vague and undetermined, than 
in any lack of certainty regarding the existence of some 
universal principle of relationship. The invariable conjunc- 
tion of a number of ^ free ' instances rules out the assumption 
of ^ chance ' ; but, in so far as the instances are left unana- 
lyzed, the precise form of the universal mode of connection 
is not exhibited in and through them. 

Where experience shows both positive and affirmative cases, 
and where at the same time it is impossible to discover any 
basis of difference for the two sets of results, we can compare 
the number of instances in which the connection obtains with 
that in which it fails. The ratio thus obtained may then be 
made the basis for calculating the probability of any particular 
event; or even of determining the likelihood that there is some 
law operative with regard to the observed phenomena (cf. 
p. 231), 



§ 54- Enumeration or Simple Counting 219 

As a matter of fact, however, Enumeration of instances is 
an aid to Induction mainly because in actual counting classifi- 
cation and analysis are also being effected. We are never 
content merely to count, taking each barely as ' one instance.' 
We also take account of the character of the instances, reject- 
ing those that are not ^ fair ' or ' typical ' and emphasizing others 
as of special or ^prerogative' importance. Moreover, the 
assemblage of instances of different types — of connection 
and lack of connection, of different races, or ages, etc., serves 
to bring out differences and similarities between groups. In 
other words, statistics, when collected intelligently and with 
some problem in view^, are really instruments of analysis; and 
in fields where experimentation is not possible, they may be 
capable of revealing, not merely the fact that certain groups 
of things are correlated, but also to some extent the character 
of that correlation. 

The conclusion which we reach, then, is that no process of 
enumeration has any claim to the title of Perfect Induction. 
.Enumeration is the beginning, rather than the end of the induc- 
tive procedure. Nevertheless, it is exceedingly useful as a pre- 
liminary step and preparation for scientific explanation. The 
number of stamens and pistils which a plant contains, or the 
number of tympanic bones possessed by an animal, is often of 
the greatest service in classification. And classification, 
although it is by no means the end of scientific investigation, 
is in many of the sciences a most essential and important step 
toward that end. The task of explaining the infinite 
variety of natural objects would be a hopeless one, if it were 
not possible to discover similarities of structure, in virtue of 
which things can be grouped together in classes. To this, 
enumeration in a very great degree contributes, especially if 



220 Enumeration and Statistics 

the counting is accompanied and directed by methodical 
thinking, so that the hkenesses and characteristics enumerated 
are not taken at haphazard, but are really important ones, and 
such as to bring out, by means of the classification, answers 
to definite questions. Enumeration thus not merely groups 
together the phenomena to be studied in a compact form, but 
at the same time begins the process of analysis, revealing 
resemblances and differences. 

§ 55. Statistics and Statistical Methods. — Statistical meth- 
ods depend upon enumeration. They aim at making the 
process of counting as exact and precise as possible. Rlimelin 
defines statistics as ^^ the results obtained in any field of reality 
by methods of counting." Modern science has come to under- 
stand that its first task must be to become acquainted, as com- 
pletely as possible, with the nature of the facts presented to it 
by experience. And, for this purpose, the careful classification 
and precise enumeration of particulars afforded by statistics 
is often of the greatest importance. ^^The extent to which the 
statistical method prevails, and everything is counted," says 
Professor Sigwart, ^^is another instance of the fundamental 
difference between ancient and modern science." ^ It would, 
of course, be impossible to enter here into a full description of 
the methods employed by statistical science. The methodol- 
ogy of every science must be learned by actual practice within 
the particular field. What we are interested in from a logical 
point of view is the purpose which statistical investigation 
seeks to fulfil, and the part which it plays in rendering our 
knowledge exact and systematic. 

We notice, in the first place, that the class of facts to which 
statistics are applied has two main characteristics: the subject 

^ Logic (Eng. trans.), Vol. I., p. 286. 



§ 55- Statistics and Statistical Methods 221 

dealt with is always complex, and capable of division into a 
number of individual parts or units; and, secondly, it is also 
of such a nature that the underlying law or principle of the 
phenomena to be investigated cannot be directly discovered. 
Thus, we employ statistics to determine the death-rate of any 
country or community, or the ratio between the number of 
male and of female births. It is clear that it is impossible to 
make use of experiment when we are dealing with facts of this 
kind, because the conditions are not under our control. If it 
were possible, for example, to determine exhaustively the 
general laws according to which the various meteorological 
changes are coordinated with their conditions, we should not 
trouble ourselves to count and register the separate instances 
of changes in the weather. Nor, if we knew exactly the general 
conditions under which any given human organism in contact 
with its environment w^ould cease to exist, should we count 
the individual cases of death. ^' In proportion as we are un- 
able to reduce the particular event to rules and laws, the 
numeration of particular objects becomes the only means of 
obtaining comprehensive propositions about that which is, 
for our knowledge, fortuitous; as soon as the laws are found, 
statistical numeration ceases to be of interest. There was 
some interest in counting how many eclipses of the moon and 
sun took place year by year, so long as they occurred unex- 
pectedly and inexplicably; since the rule has been found 
according to which they occur, and can be calculated for 
centuries past and to come, that interest has vanished. But 
we still count how many thunder-storms and hail-storms 
occur at a given place, or within a given district, how many 
persons die, and how many bushels of fruit a given area pro- 



222 Enumeration and Statistics 

duces, because we are not in a position to calculate these 
events from their conditions." ^ 

In cases like those mentioned above, where we are as yet 
unable to determine the general laws which are at work, we 
call to our aid statistical enumeration. There are three main 
advantages to be derived from the employment of this method. 
In the first place, it contributes directly towards a clear and 
comprehensive grasp of the facts. Instead of the vague im- 
pression derived from ordinary observation, statistics enable 
us to state definitely the proportion of fine and rainy days 
during the year. Statistical enumeration is thus one of the 
most important means of rendering observation exact and 
trustworthy, and of summing up its results in a convenient 
and readily intelligible form. It is of the utmost importance, 
when dealing with complex groups of phenomena, to have a 
clear and comprehensive view of the facts of the case. Thus, 
when trying to understand the nature of society, it is neces- 
sary to determine accurately, by means of statistics, such 
facts as the number of male and of female births, the death- 
rate, the proportion of marriages, the age of marriage, etc. 
This may be regarded as the descriptive use of statistics. In 
the second place, by giving us the average in the past for 
large numbers of things or events occurring within certain 
lengths of time, in areas of space, statistics enable us to form 
probable judgments as to what will happen in the future in 
cases where we cannot predict because the causal laws are 
unknown or are too complex. This second use will be dis- 
cussed in § 52. But, in the third place, statistics often serve 
to reveal quantitative correspondences or uniformities be- 
tween two groups of phenomena, and thus suggest that some 

■^ Sigwart, Logic (Eng. trans.), Vol. II., p. 483. 



§ 55- Statistics and Statistical Methods 223 

causal connection exists between them. It is found, for ex- 
ample, that the number of births in any given country varies 
inversely as the price of food during the previous year. Now, 
this fact at once suggests the existence of certain physio- 
logical and psychological laws which may serve to bring 
these facts into causal relation. In many cases, such cor- 
respondences serve only to confirm our expectation of the 
presence of a causal law, which is based on other grounds. 
Thus we should naturally expect that there would be a rela- 
tively greater number of cases of fever in a town which had 
an insufficient water supply, or an antiquated system of sew- 
erage, than in a town where these matters were properly pro- 
vided for ; and statistics might bear out our conclusions. In 
general, however, it may be said that causal laws are sug- 
gested, not by corresponding uniformities, but by correspond- 
ing variations, as shown by the statistics of different sets of 
facts. So long as the death-rate, for example, shows a con- 
stant ratio to the population, no causal inference is suggested; 
but if the annual number of deaths increases or decreases 
considerably, we are led to look for some variation from the 
normal in some coincident group of phenomena. And if it 
is found that the variation in the death-rate has been accom- 
panied by unusually favourable or unfavourable conditions 
of weather, the presence or absence of epidemics, or any 
similar circumstances, there will be at least a presumption that 
a causal relation exists between these two sets of events. — 
From a certain likeness or quantitative resemblance between 
the variations of two distinct classes of phenomena, we are 
led to the hypothesis of their causal connection. 

In this use of statistics, they become directly auxiliary to an 
explanation of the facts they enumerate. But the correlation 



224 Enumeration and Statistics 

and causal connection of the facts come to light only when 
looked for. Merely to count, without any definite purpose, 
would never help us to explain. As we saw in the last chapter, 
induction always proceeds under the guidance of conceptions 
or general ideas. We do not simply stare, as it were, at the 
facts we examine, but we look at them to discover their 
meaning and select such of them as are relevant or significant 
in the light of some general theory or conception. In other 
words, we examine the facts to put theories (which may, of 
course, be very vague as yet) to the test, or to get answers to 
certain questions which we have in mind. Now this is just 
as true of enumeration and statistics as it is of the other 
methods of induction. As has already been remarked of 
enumerative classification, we must decide what it is worth 
while to count in the particular field in which we are count- 
ing. The questions that we wish answered will determine 
this. And even when we have our figures, they will be 
meaningless or even altogether misleading unless we know 
how to interpret them. It is the neglect of such considera- 
tions that leads to the misuse of statistics and the frequent 
contradiction of the statement that ^ figures cannot lie.' 

(i) It is true that on a superficial view of the statistical method 
the figures may seem at times to arrange themselves in definite 
groups quite apart from any intellectual labour save that of mere 
counting. Thus it might seem that in taking the average rate of 
mortality on the basis of the returns of local ofiicials, etc., the 
figures of themselves disclosed the fact that the rate was higher for 
infants under two years of age than in later periods of life. But 
the total average of deaths would never have shown this. It is only 
because the average for infants has been separately calculated, in 
the expectation that there might be a difference, that the difference 



§ 55- Statistics and Statistical Methods 225 

has been found. The tentative question — Is there, as we have 
reason on the ground of unsystematic observation to beHeve, a 
striking difference between the death-rate of infants and that of 
older persons ? — is thus answered in the affirmative. 

But the function of guiding ideas and hypotheses becomes even 
more important when the statistics are to be used directly in the 
service of explanation. Two examples will serve to make this 
plain. The first is from Professor Sigwart: ^^The position of a 
barometer in a given locality passes from day to day, and from 
month to month, up and down through all possible variations, in 
which w^e can at first find absolutely no rule (though they have a 
constant mean value). . . . But if we calculate the average for the 
particular hours of the day over a considerable time, we find a 
periodical variation between two maxima and minima with respect 
to the general average. . . . That the period is daily points to 
the influence of the sun. ... But unless we had conjectured 
that the different positions of the sun, and the changes brought 
about by them, had some influence, we could not have thought of 
summing up the particular hours of the day apart from each 
other.'' ^ In this case, the constant average first obtained told us 
nothing, except that the conditions, whatever they were, which 
governed the fluctuations of the barometer, remained constant on 
the whole. But when an hypothesis was found, and the varying 
positions divided into groups of such a nature that their com- 
parison could test it, we obtained a partial explanation of them. 

Again, suppose that we are gathering statistics of the divorce- 
rate in various states and countries. The figures, unanalyzed, 
would tell us little. But suppose we had a definite problem in 
mind, such as the effect of laws on the frequency of divorce. What 
would we do with our figures? ^^ First, select states or countries 
with similar social and economic conditions, but very different 
laws, and compare their divorce-rate; do the same for states 

^ Logic, Eng. trans., Vol. II., pp. 496-497. 



226 Enumeration and Statistics 

with similar laws, but different economic conditions ; note whether 
the divorce-rate varies with the law, or with the other factors, or 
with neither exclusively. Secondly, examine every instance of a 
change in the divorce law, and observe whether it was attended by 
a change in the figures such as might have been produced by the 
law."^ Here again there is a division of the phenomena into 
groups distinguished by some difference in the supposed cause, 
and then a comparison of these groups. The methods employed, 
as we shall see presently, are essentially those of Agreement and 
Difference, and of Concomitant Variations. 

In general, then, there are two things to be said about the use of 
statistics. In the first place, the smaller and more numerous the 
groups are into which the enumerated phenomena are divided, and 
the more exactly the rules of division in general are followed in 
doing this, the more valuable, other things being equal, the statistics 
will be. In the second place, it is by the comparison of these 
groups that statistics aid us to discover causal relations. The 
kind of groups we shall make, and the points in which we shall 
compare them, are determined by the questions we have to ask, or 
the tentative conceptions we have to test. In all these respects 
the use of statistics is governed by the general principles of the 
inductive method, which consists essentially in the analysis and 
comparison of phenomena in the light of an hypothesis. 

(2) Statistical enumeration is frequently employed to determine 
the average of a large number of instances of a particular kind. This 
is obtained by dividing the sum of the given numbers by the num- 
ber of individuals of which account is taken. In this way a general 
average is reached which does not necessarily correspond exactly 
with the character of any individual of the group. It represents a 
purely imaginary conception, which omits individual differences and 
presents in an abbreviated form the general character of a whole 
class or group. In this way, by the determination of the average, it 

^ Willcox, The Divorce Problem^ p. 41. 



§ 55- Statistics and Statistical Methods 227 

becomes easier to compare complex groups with one another. Thus, 
when the average height of Frenchmen and Englishmen has been 
determined, comparison is at once made possible. From the mean 
or average of a number of individuals, or set of instances, however, 
we can infer nothing regarding the character of any particular indi- 
vidual, or of any particular instance. What is determined by the 
method of averages is the general nature of the group, as represented 
by the average or typical individual. But this method does not 
enable us to infer anything regarding the character of any member 
of the group. A, or B. 

Indeed, the simple arithmetical mean or average by itself may 
give us quite an erroneous idea of the general character of the indi- 
viduals or instances which make up the group. For example, if 
ten divorces were granted in a county, eight at the end of three 
years of married life, one at the end of six, and one at the end 
of thirty, it would give quite a misleading notion to say that the 
average duration of marriage in couples seeking divorce there was 
six years. In order to correct such defects in the use of the average 
by itself, especially in applying the statistical method in biology, 
two other expressions are now used, the mod^e and the median 
value. The mode is the condition which occurs most often in the 
group examined; in the example just cited it would be three years. 
The median value is the condition of the individual at the middle 
of the series, when it is arranged in order. In this case it approx- 
imates to the mean. When the group is symmetrically distributed 
about the average, these three expressions are approximately the 
same ; but as it becomes less evenly distributed, they differ more or 
less widely, and now one of them, now the other, may give a better 
notion of the character of the group than the average by itself 
would. All three expressions, however, are primarily expressions 
for the general nature of the group; and the information they 
give us concerning the nature of any individual member of it is 
always indirect, imperfect, and uncertain, save as we are informed 



228 Enumeration and Statistics 

where in the group the member occurs. There are also occasions 
when it is preferable to use the geometrical mean. 

§ 56. The Calculation of Chances. — We still have to con- 
sider the second of the three uses of statistics mentioned in 
the foregoing section. As has been said, statistics not only 
help us in describing and in explaining complex phe- 
nomena, but they are also used to enable us to judge what 
will be true, on the whole, of a long series of events, in cases 
where ignorance of the causal laws concerned prevents our 
making predictions concerning the individual members of 
the series, when taken separately. This is usually called 
the calculation of chances, or probabilities. Now there is, 
of course, no such thing as ^chance,' regarded as a power 
which controls and governs events. When we speak of some- 
thing happening ^by chance,' or of some occurrence as 
' probable,' we are expressing merely a deficiency in our own 
knowledge. '^ There is no doubt in lightning as to the point it 
shall strike; in the greatest storm there is nothing capricious; 
not a grain of sand lies upon the beach but infinite knowledge 
would account for its lying there; and the course of every 
falling leaf is guided by the same principles of mechanics as 
rule the motions of the heavenly bodies." ^ To assert that 
anything happens by chance, then, is simply to confess our 
ignorance of the causes which are operative. 

It is clear that w^e are in this position regarding many of 
the ordinary events which belong to the future. Because 
of my ignorance of the causes at work, I can only say, ' It 
may rain to-morrow.' It is impossible to tell upon which 
side a penny will fall at any particular throw, or what card 
may be drawn from a pack. But in cases like these, we have 

^ Jevons, The Principles of Science^ Vol. I., p. 225. 



§ 56. The Calculation of Chances 229 

to accept, for lack of anything better, a numerical statement 
of the chances for any particular event. Thus we know 
that, since there are only two sides upon which a penny can 
fall, the chances of throwing heads in any trial is |-. Simi- 
larly, there are four chances out of fifty-two of drawing an 
ace from a pack of cards. The chance of obtaining an ace 
by any draw is therefore -^^ = ^^, These figures express the 
mathematical chances. Experience of a limited number of 
instances may, however, sometimes appear to show a lack 
of hannony between the mathematical and the actual chances. 
But in proportion as the number of trials is increased, the 
result is found to approximate more and more nearly to the 
mathematical expectation. In twenty throws of a penny 
or a die, we should not be surprised to find that the result 
differed from the fraction expressing the mathematical 
chances. But this discrepancy would tend to disappear as 
the number of cases was increased. Jevons illustrated this 
by actual trial, using a number of coins at a time. Out 
of a total of 20,480 throws, he obtained a result of 10,353 
heads. On the result of the experiment he remarks: ^^The 
coincidence with theory is pretty close, but considering 
the large number of throws there is some reason to suspect 
a tendency in favour of heads.'' ^ 

Apart from the simple and somewhat artificial cases 
where we are concerned with coins and dice, etc., it is impos- 
sible to determine with mathematical precision the chances 
for or against any event, since the possibilities are indefinite 
as well as the causes. In cases where the whole series of 
possibilities does not lie before us, we have to base our cal- 
culations for the future on what is known regarding the fre- 

^ Jevons, op. cit.y Vol. I., p. 230. 



230 Enumeration and Statistics 

quency with which the events under consideration have 
occurred in the past. Now the results of the last paragraph 
make it clear that it is of the utmost importance that the 
statistics, which are taken as the basis, shall be as full and 
comprehensive as possible. It is evident, for example, that 
serious errors would be likely to arise, if the death-rate for 
a single year, or for a single county or tov/n, were taken 
as typical of the country as a whole. To render statistics 
trustworthy, they must be extended over a considerable 
period of time, and over a large extent of country, so as to 
eliminate the accidents due to a particular time or to a 
particular locality. 

(i) When this has been done, however, and statistics have been 
obtained that have a right to be regarded as really typical, the 
chances in any individual instance regarded simply as one member 
of a large group, and apart from its own special characteristics, can 
be readily shown. Thus we fmd that out of one thousand children 
born, about two hundred and fifty die before the age of six years. 
The chances, then, at birth, that any child will reach this age, are 
tWo ^^ f • Again, it is found that only about two persons in one 
thousand live to be ninety years old. So that the probability of 
any child living to this age would be expressed by the fraction y-oV^ 
or -5^. Such probabilities are simply averages which briefly de- 
scribe what has happened in the past. Now what has happened in 
the past in a large number of cases we naturally expect to happen 
in the future. This is essentially the principle upon which life- 
insurance companies proceed. Their business is conducted on 
the assumption that there will be an approximately constant 
death-rate, though they cannot foretell what particular individuals 
are to die in any year. It thus becomes possible to calculate 
what losses from death may be expected each year. Suppose 
that it is found that the annual death-rate among men of a certain 



§ 56. The Calculation of Chances 23 1 

age throughout the country is twenty out of every thousand. If 
each man's life were insured for $1000, the loss to the company 
from this source would be $20,000. To compensate for this loss, 
the company would be obliged to demand an annual payment of 
$20 from each of the one thousand individuals in the class. Of 
course, the actual computations upon v/hich insurance is based 
in concrete cases are vastly more complex than this, and many 
other considerations arise of which account has to be taken. But 
the general principle involved is, that by taking a sufnciently large 
number of cases, chance can be almost eliminated. We can have 
no means of determining whether any healthy individual will or 
will not die before the end of the year. There would be a very 
serious risk, amounting practically to gambling, in insuring his 
life alone, for probabilities are essentially averages. They inform 
us about the group, and not directly about any particular mem- 
ber of it. But the transaction, as we have seen, is no longer a 
mere speculation when a large number of individuals are con- 
cerned; for the actual loss can be accurately foretold and pro- 
vided for. 

(2) As precise an analysis of the conditions as is possible is as 
important in estimating probabilities as it is in the other uses of 
statistics. The smaller the group of which the average is taken, 
and the more definite the information we have about it, the more 
accurate our estimate becomes. It is not enough, for example, 
for the purposes of life-insurance, to know what the average age 
of death is, all adults being taken as on the same footing. What 
the insurance companies do is, in the first place, to exclude all who 
are not in fairly good health, and who may be in danger of heredi- 
tary disease, from their membership ; and, in the second place, to 
calculate the average number of years of life remaining to men of 
different ages. Every individual is thus put into a special class, 
and the premium calculated accordingly. 

(3) A rather common fallacy is to suppose that the known prob- 



232 Enumeration and Statistics 

ability of any particular event of a group or series, gives us some 
ground for expecting this when the other events of the series have 
occurred. But it should be remembered that the known prob- 
ability affords no such ground of inference, except as we know 
that there is some causal relation between these events; and 
then we are not reasoning by probabilities. The probability of 
throwing double six with two dice, for example, is -^-^. But because 
in 35 consecutive throws the double six has not appeared, it does 
not follow that it is any more likely to do so on the 36th throw than 
it was on the first. The probability is still -3^^-, and so continues. 
If we take a suf35ciently large number of throws, as has already 
been remarked, we shall find that the double six has, on the average^ 
appeared once out of every 36 throws. But we cannot foresee 
whether the appearances of the double six sufficient to give this 
average will be evenly distributed through the whole series of 
throws, or occur in irregular sequences. 

(4) A peculiar use of the theory of probability in order to dis- 
cover causal connections between events is possible on the principle 
just stated. When we are in doubt, that is, as to whether two 
events are in any way causally connected, we can by collecting 
statistics estimate the probability of their appearing together on the 
assumption that they have no causal relation. Then if they are 
found to appear together more or less frequently than this esti- 
mate, we are justified in assuming that there is some causal rela- 
tion between them. Suppose, for example, we are studying two 
characteristics which occasionally appear in a certain species of 
animal, and wish to determine whether they have any essential 
connection. We find on examining a large number of cases that 
one of these characteristics appears once in every sixteen individ- 
uals, on the average, and the other once in every twenty. If 
there is no connection between them, then, on the theory of 
probability, the chance of their happening together is 3^^. But 
if we found that they occurred together in 20 cases out of every 



§ 56. The Calculation of Chances 233 

100, we should conclude that there must be some cause or causes 
common to both characteristics, or else that one of them in some 
way depends on the other. 

REFERENCES 

C. Sigwart, Logic ^ §§ loi, 102. 

J. G. Hibben, Inductive Logic^ Ch. XV. 

L. T. Hobhouse, The Theory of Knowledge, Pt. II., Ch. XI. 

J. S. Mill, Logic, Bk. III., Ch. XVIII. 

B. Bosanquet, Logic, Vol. I., pp. 128 jff. 



/ 

CHAPTER XVI 

DETERMINATION OF CAUSAL RELATIONS 

§ 57. Causal Connection. — So far, we have been dealing, 
primarily, with observational methods, and with the results 
obtained through the enumeration of particular things. We 
have been considering how our knowledge of the qualities 
and quantities of objects may be made as exact and com- 
plete as possible, but we have not discussed in detail the 
methods by which we discover the connection of things. 
But all Inductive thinking, as has been shomv-is based 
on the assumption that there are universal forms or prin- 
ciples of relation according to which things are connected 
in a systematic way. We cannot really be said to know 
at all, until we become aware that certain parts of our 
experience are united, like the links of a chain, one part 
involving another. And, as has been already frequently 
pointed out, the growth of knowledge is constantly bringing 
to light new connections between facts that were previously 
taken to be independent of one another. Now, it was also 
stated in an earlier chapter (§51), that the connections and 
relations of things may be conceived in different ways— that 
there are various ^categories of experience.' Naturalscience, 
however, in describing and explaining the relations of things, 
does so primarily in terms of Cause and Effect. All phenomena 
without exception, it is assumed, are causally dependent on 
other phenomena; everything which happens has its cause, 
and is in turn followed by its effect. From the standpoint of 

234 



§ 57- Causal Con7iection 235 

practical experience, also, we are constantly obliged to look 
for causes ; for only where the cause is known is there any 
certain method of producing the effect. The determination 
of causes, then, is one of the most essential problems of Induc- 
tion, the category of Cause and Effect being perhaps the 
most universal and important category by means of which 
the parts of our experience are thought as related according 
to universal laws. What rule, or rules, can now be given 
which will enable one to discover what is the cause or the effect 
of an event in any particular case ? 

Before we proceed to the answer of this question, however, 
it is necessary to explain briefly what is meant in the natural 
sciences by the relation of cause and effect. In the first 
place, the natural sciences regard the world as consisting 
of a phenomenal order of events. In other words, they 
are concerned with the particular things and changing 
events that appear or show themselves in ordinary experi- 
ence. Both the inner and the outer world appear to be 
composed of an indefinite manifoldness of particular things, 
events, occurrences. Now, the natural sciences do not ask 
whether this aspect of the world is ultimate Reality or merely 
Appearance. The problem of the scientist is rather to set 
out from the manifold objects and events as they appear in 
ordinary experience, and to seek to describe and explain them 
by showing how they are related in various complex ways 
through principles of causal dependence. It is assumed 
that each phenomenon of which the world is composed, is yet, 
in spite of the independent and separate existence which it 
seems to have, connected through the principle of causality 
with something else which determines it, or is in some way 
necessary to its existence. Every event, that is, has its cause. 



236 Determination of Causal Relations 

The explanation of every phenomenon is to be found in 
something external to it, but upon which it is dependent. The 
relation of cause and effect assumes that all phenomena are 
externally determined ; or, as the same thing is often expressed, 
it assumes a mechanical relation between the different parts 
of the world. Moreover, this relation is, as has been said, 
simply a special form, or category, through which the uni- 
versal relations of things are expressed. That there are 
universal modes of connection, and that ^ once true always 
true,' is a law or postulate of all thinking. Causality, 
being as we have seen one very definite and useful way of 
thinking that relation, is accordingly of the greatest im- 
portance, both for science and practical life. 

(i) When the general postulate of all thinking, that things shall 
hold together systematically so as to be intelligible, is put in more 
definite form as the law of Cause and Effect between phenomena, 
we get the notion of the Uniformity of Nature. Of course, strictly 
speaking, the Uniformity of Nature is involved in the fundamental 
postulate of thought that things hang together in a rational way. 
Nevertheless, the conception is usually taken to imply the absolutely 
invariable sequence of causal events. From the point of view of 
natural science, Nature is uniform in the sense that all instances of 
the same phenomenon P, are always determined in the same way by 
the same cause Q. This, then, is really mechanical uniformity. 
The relation between P and Q is not only external or mechanical, 
but absolutely fixed and invariable. The conception of any 
'spontaneous variation/ any modification without an externally 
determining cause, is completely excluded. 

(2) In speaking of any phenomenon as having a cause, the relation 
has, of course, been artificially simplified. In reality, there are 
always a number of * causes,' or determining conditions necessary to 



§ 58. MiWs Experimental Methods 237 

the occurrence of any event. What we mean by ^the cause,' in 
any particular case, depends mainly on the character and purpose of 
the inquiry. In practical life the ' cause ' sought for is usually some- 
thing that can be employed directly as a means to the desired result. 
And even in scientific inquiries practical motives continue to play a 
part in deciding what shall be regarded as the ^ essential ' or ^ real' 
cause of any phenomenon. The cause is that which can be em- 
ployed to produce the desired effect, and so to afford practical mas- 
tery over the situation. This direct reference to practice, however, 
is not essential to the idea, which is primarily a way of thinking 
things in relation. Ultimately, then, the * real' or * essential ' cause 
is that which shows most clearly the character of the relationship 
between two phenomena — that which, in a sense, is the sum or 
synthesis of all the conditions. 

The cause, then, from the point of view of science, is that with- 
out which the phenomenon would not occur. It is also sometimes 
defined as ^the invariable and necessary antecedent,' while the 
effect is spoken of as the ^invariable consequent.' In using these 
terms, however, it must not be supposed that the cause always and 
necessarily precedes the effect in time. The relation of cause and 
effect is not to be regarded as merely temporal. 

§ 58. Mill's Experimental Methods. — The methods by 
which causes and effects may be determined were formulated 
by Mill in his Logic. He stated, in general terras, the prin- 
ciples which were already in use in scientific procedure. Mill 
gives five separate canons, but, as he himself recognizes, 
there are but two main principles involved. ^' The simplest 
and most obvious modes of singling out from among the 
circumstances which precede or follow a phenomenon, those 
with which it is really connected by an invariable law, are 
two in number. One is, by comparing together different in- 
stances in which the phenomenon occurs. The other is, by 



238 Determmation of Causal Relations 

comparing instances in which the phenomenon does occur, 
with instances in other respects similar in which it does 
not. These two methods may be respectively denominated 
the Method of Agreement and the Method of Differ- 
ence." ^ Of the other three methods mentioned by Mill, 
one — the Joint Method of Agreement and Difference — is, 
as the name implies, a direct combination of the first two, 
while the Method of Residues and the Method of Concomi- 
tant Variations are corollaries from the same principles. 

The purpose of these comparisons is to exhibit and define 
the true cause. This is accomplished by proceeding directly 
through negation. That is, the other circumstances which 
could be supposed to have any influence are successively 
eliminated. And, as already pointed out (§ 50), it is just with 
a view to the possibility of elimination, that the instances 
are selected. Since the cause is that without which the phe- 
nomenon would not occur, the rules of elimination follow im- 
mediately: (i) That is not the cause of a phenomenon in 
the absence of which the phenomenon occurs; (2) That is 
not the cause of a phenomenon in whose presence the phenom- 
enon fails to occur; (3) That is not the cause of a phenome- 
non which varies when it is constant, or is constant when it 
varies, or varies in no proportionate manner with it.^ 

The process of eliminating the other things that could 
conceivably be causes, also defines the sphere and nature of the 
true cause. The preceding rules, then, might have been 
stated positively, and it is this positive side of the process that 

^Mill, Logic, Bk. III., Ch. VIII., § I. 

2 These statements are essentially those given by Joseph {Ah Introduction 
to Logic, pp. 403-404), who, however, adds a fourth supplementary rule: 
"Nothing is the cause of one phenomenon which is known to be the cause 
of a different phenomenon," 



§ 59- '^^^^ Method of Agreement 239 

has been emphasized by Mill. It is important to bear in 
mind^ however, in studying MilPs Methods of Experimental 
Inquiry^ that elimination or negation plays an important 
part in the process which he describes. We shall now pro- 
ceed to state and illustrate the canons of the different methods. 
§ 59. The Method of Agreement. — The principle upon 
which this method proceeds is stated in the following way 
by Mill: ^^ If two or more instances of the phenomenon under 
investigation have only one circumstance in common^ the 
circumstance in which alone all the instances agree is the cause 
{or effect) of the given phenomenon^ The purpose of this 
rule, it will be remembered, is to help us to determine what 
particular facts in our experience are connected as causes and 
effects. If the problem is to find the cause of some phenome- 
non, the canon may be illustrated in the following way. Let 
P^ P^, P^, represent different instances of a phenomenon, 
P, whose cause is to be ascertained. And suppose that we are 
able to analyze, 

the antecedents of P^ into abed; 
the antecedents of P^ into gfcm; 
the antecedents of P^ into klnc. 

Now it is clear that c is the sole circumstance in which the 
antecedents of all these instances of P agree. And nothing 
can be the cause of P in the absence of which P still occurs. 
We should be justified in concluding, therefore, according to 
this method, that c is probably the cause of the phenomenon 
under investigation, P. We may, then, adopt Jevons's 
formula for discovering the cause of any given phenomenon by 
this method : ' The sole invariable antecedent of a phenomenon 
is probably its cause, ^ 



240 Deterfnination of Causal Relations 

If, now, we wished to discover the effect of something which 
happens, it would be necessary to determine, by observing 
a number of instances, what common circumstance can be 
found among the events which follow it. 

If Q^ were followed by f^h^ 
and Q^ were followed by Imgc^ 
and Q^ were followed by grst^ 

we should be able to say that Q and g were connected as cause 
and effect. The rule might then be expressed: The sole 
invariable consequent of a phenomenon is probably its effect. 

When antecedents and consequents are thus represented 
schematically by means of letters, it is easy to perceive at 
once the common circumstance in a number of instances. 
But the facts and events of the real world are not separated 
off from each other in this way. The common circumstance 
in which a number of instances agree has to be separated out 
by analysis from the variable elements which form part of the 
different antecedents and consequents. Moreover, an essen- 
tial part of the work of Induction consists in selecting in- 
stances such that all the possibilities — all the things that might 
be connected with P — are included. It should also enable 
us to recognize the common element as common, though it 
may appear in wholly different circumstances. The way in 
which the work of analysis proceeds will become more evident 
by considering a number of concrete cases in which this 
method may be employed. 

If a number of cases of typhoid fever were to appear at 
about the same time in a community, one would naturally 
wish to explain this phenomenon by tracing it to its cause; 
and to do this one would try to discover some circumstance 



§ 59- ^^^^ Method of Agreement 241 

which was the common antecedent of all the cases. Knowing 
from the records of past experience that the cause is to be 
sought for among a limited number of circumstances, one 
would select the various instances with the purpose of testing 
the different possibilities. The water supply might first be 
examined. But if it were found that this was derived from 
entirely different sources in the different cases, we should 
probably conclude that the explanation must be sought else- 
where. Suppose that as a result of careful analysis it were 
discovered that all the individuals prostrated with the fever 
had eaten oysters bought at the same market. If this were the 
only common circumstance discoverable after careful investi- 
gation, we should conclude that probably the oysters were the 
cause of the fever. The process of analysis could be pushed 
still further, if one wished, in order to determine more exactly 
the precise source of the infection; e.g, it might be found, as a 
result of further inquiry, that the water in which the oysters 
were kept was vitiated by a sewer. 

Another example of the method of agreement which is 
often quoted by logicians may be given. One would natu- 
rally suppose that the colours and lines of mother-of-pearl 
were due to the chemical or physical character of the sub- 
stance itself. Sir David Brewster, however, happened to 
take an impression of a piece of mother-of-pearl in beeswax 
and resin, and was surprised to see the colours reproduced 
upon its surface. He then took a number of other impressions 
in balsam, gum-arabic, lead, etc., and found the iridescent 
colours repeated in every case. In. this way he proved that 
the colours were caused by the form of the substance, and not 
by its chemical qualities or physical composition. The differ- 
ent substances, wax, balsam, lead, etc., in which the phenome- 



242 Determination of Causal Relations 

non of colour appeared, had nothing in common except the 
form. This, therefore, according to the method of agreement, 
was properly regarded as the cause of the phenomenon to be 
explained. 

An example of the application of this method to the discovery 
of the effect of a phenomenon may now be given. Let us 
suppose that the problem is to determine the effect of some 
proposed legislation. It is necessary, of course, to refer to 
other instances where this legislation has been put in force, 
and our general information about political and social affairs 
shows more or less definitely what kind of connected circum- 
stances it is worth while noting. Let us suppose that in one 
case what followed the enactment of the law under considera- 
tion was a falling off of revenue, an increase of immigration, 
large exports, etc., and in a second, the revival of ship-building, 
decrease of crime, and increase of immigration; and that in 
other instances where still other conditions prevailed, the 
number of immigrants still continued to increase. Since this 
latter circumstance is the only one which follows invariably 
upon the enactment of the law, we are justified in concluding, 
after a certain number of observations, that it is necessarily 
connected with the law as its result. 

It is important to note that the conclusions reached by this 
method are greatly strengthened by increasing the number of 
observations, and by taking as many instances as possible 
that are dissimilar in character. By so doing, the real 
cause is more hkely to be included among the antecedents 
noted, and, at the same j:ime, the probability is lessened that 
the connection between antecedent and consequent is a 
merely accidental conjunction. But even when such pre- 
cautions are taken, the method of Agreement does not afford 



§ 59- ^^^^ Method of Agreement 243 

any very definite knowledge. By eliminating the other ante- 
cedents, we found that c is probably connected causally with 
P. But c is left as a mere unanalyzed ' circumstance/ e.g, 
^the drinking water,' ^ the form' of the substances which 
showed iridescent colours, etc. Just how the connection takes 
place, whether it be direct or indirect, is not shown. It is 
clear, then, that further analysis is necessary in the interest of 
scientific knowledge. The method of Agreement, although 
perhaps in some cases yielding results sufficiently exact for 
practical application, merely suggests a problem for further 
scientific inquiry. Its defect, as we have seen, is that it does 
not sufficiently get beneath the surface of things so as to make 
certain and definite their mode of relation. 

It may be well to notice under separate headings some of the 
special difficulties which result from this method's superficial mode 
of analysis. 

(i) Reciprocity of Phenomena. So long as we are dealing with 
events which succeed one another in time, there is no difficulty in 
perceiving which is cause, and which effect. But we are often 
called upon to investigate the relation between phenomena that 
do not appear as successive, but as co-existent. And it is then not 
at all easy to determine by means of the method of Agreement 
which is cause and which is effect. Poverty and intemperance, for 
example, are found conjoined so frequently as to make it probable, 
apart from other considerations, that some causal relation exists 
between them. It might be maintained with apparently equal 
show of reason, that the former is the cause, or the effect, of the 
latter. Again, is one to say that ignorance is the cause or the effect 
of moral degradation ? There seems to be no means of determin- 
ing by this method which is antecedent and which consequent. 
As a matter of fact, it is probably true in such cases that the phe- 
nomena act and react upon each other: that each term, in other 



244 Determination of Causal Relations 

words, is at once both cause and effect. In such instances we go 
beyond the conception of causal dependence in one direction, to that 
of the Reciprocity of phenomena. 

(2) Complexity of Phenomena. Again, neither the cause nor the 
effect need be composed of a single phenomenon, as the method 
seems to assume. Indeed, as further observation shows, the ante- 
cedents and consequents which the method of Agreement takes as 
'single circumstances' are usually very complex. The difficulty is 
that the process of analysis has not been carried far enough to bring 
out the essential point involved. Everything is lumped together 
and the exact nature of the connection left vague and uncertain. 
Thus, for example, the ' ill-health ' of a community might be shown 
by this method to be related causally to the 'sanitary conditions.' 
Here it is obvious that both antecedent and consequent involve com- 
plex relations and conditions, which are left vague and ill-defined. 

(3) Plurality of Causes. There is still another circumstance that 
renders uncertain the results of the method of Agreement. In 
itself, it can only show that c is a cause of P, not that it is the only 
or necessary cause. Taking the word ' cause ' in its popular sense, 
we cannot say that a given phenomenon is always produced by 
the same cause, or that the effects of different causes are always 
different. Intemperance may result from different causes in 
different cases, or heat may be generated through combustion, 
friction, or electricity. The fact here illustrated, that an effect 
may be produced by any one of several causes, is what is meant by 
the phrase 'Plurality of Causes.' Once more, this defect is 
simply the result of a too vague or superficial analysis. When 
analysis can discover what has really occurred, what the real nature ^ 
of the effect is, it becomes possible to determine the nature of the 
only and essential cause. 

§ 60. The Method of Difference. — According to the 
method of Agreement, we compare a number of diverse in- 
stances, in all of which a given phenomenon occurs, and en- 



§ 6o. The Method of Difference 245 

deavour to discover the one circumstance which is invariably 
present. The method of Difference, on the other hand, com- 
pares an instance in which a phenomenon occurs with another 
as nearly similar to it as possible, in which it does not occur. 
Its canon is expressed by Mill as follows: ^^7/ an instance 
in which the phenomenon under investigation occurs^ and an 
instance in which it does not occur ^ have every circumstance in 
common save one, that one occurring only in the former; the 
circumstance in which alone the two instances differ is the effect, 
or the cause, or an indispensable part of the cause, of the 
phenomenon y It will perhaps make the matter clearer to say : 
^That which is present in a case when a phenomenon occurs, 
and absent in another case vv^hen that phenomenon does not 
occur, all other circumstances remaining the same in the two 
cases, is causally connected with that phenomenon.' That is, 
by means of this method we compare two instances which 
differ only in the fact that the phenomenon in which we are 
interested, is present in the one, and absent in the other. 
If now the two cases are represented in this way, 
PHK conjoined with alg, 
and HK conjoined with Ig, 
we conclude at once that P is causally connected with a. Our 
selection of P, or the element in question, as the supposed 
cause, is, of course, made in accordance with an hypothesis or 
general notion of what the possible or likely causal relations 
in the subject under investigation are, gathered from previous 
experience. If this notion is as yet too vague to give us any 
definite guidance, then we are obliged to analyze the phenom- 
ena as exactly and minutely as we can, and experimentally 
vary the circumstances in every conceivable way, until the 
requirements of the method are, if possible, satisfied. 



246 Determination of Causal Relations 

Almost any instance in which experiment is employed will 
serve to illustrate this method. If a bell is rung in a jar 
containing air, the sound will, of course, be heard at any ordi- 
nary distance. But after having removed the air by means of 
an air-pump, let the bell be again struck. It will now be 
found that the sound is no longer heard. When the two cases 
are compared, it is at once evident that the only difference in 
the antecedents is the presence of the air in the one case, and 
its absence in the other. When the air was present, the 
sound was heard; when it was absent, the sound was not heard. 
We conclude, therefore, that the perception of sound is caus- 
ally connected with the presence of atmospheric air. Again, 
we can prove that the so-called ^ taste' of different objects 
depends upon smell, by tasting, say, an orange, and after a 
little time has elapsed, tasting it a second time while holding 
the nose. It will be found in this latter case that instead of 
the familiar ^ orange taste,' one senses merely ^ acid,' or ^ sweet.' 
The only difference in the two trials being that in the former 
the organ of smell, which was excluded in the latter, was oper- 
ative, it follows that the so-called ^orange taste' is proved 
to be due to smell rather than to taste proper. 

An essential requirement of the method of Difference is 
that only one circumstance shall he varied at a time. The 
object of the method is to isolate the various conditions which 
go to make up a complex phenomenon, in order that we may 
mark the effect of the presence or absence of each one individ- 
ually. Now, in observing what goes on in nature, we rarely 
find changes in which but a single element has varied. If 
we find that to-day is cooler than yesterday, we may be in- 
clined to refer the change to the thunder-storm of last night. 
But rain also accompanied the thui^ider-storm, and the direc- 



§ 6o. The Method of Difference 247 

tion of the wind has changed. So that it is impossible in 
such cases to apply the method of difference. To employ this 
method successfully, observation usually must be supple- 
mented by experiment. In performing experiments, we 
determine what conditions are to be operative, and arrange 
the apparatus so as to carry out our purpose. Having thus 
control of the conditions, we are able to vary them at pleasure. 
In this way, experiment becomes an instrument by means of 
which analysis can be carried further than is possible for un- 
aided observation. It enables us to separate things which are 
usually conjoined, and to observe the result of each when 
taken by itself. In employing experiment, however, the 
greatest care must always be taken to introduce or remove 
only one condition at a time, or at least only one new circum- 
stance which can in any way influence the result. 

It often happens, too, as Jevons points out, that the ex- 
perimenter is not aware of all the conditions which are opera- 
tive when his investigations are made. ^ Some substance 
may be present, or some power may be in action which escapes 
the most vigilant examination. Not being aware of its 
existence, we are of course unable to take proper measures to 
exclude it, and thus determine the share which it may have 
in the results of our experiments.' ^ For this reason, it is 
always necessary that experiments should be repeated by 
different persons, and so far as possible under varying condi- 
tions. I quote two examples from the work of Jevons to 
which reference has just been made. 

^* One of the most extraordinary instances of an erroneous opin- 
ion due to overlooking interfering agents is that concerning the 
increase of rainfall near the earth's surface. More than a century 

^Jevons, Principles of Science , Vol. II., p. 37. 



248 Determination of Causal Relations 

ago it was observed that rain gauges placed upon church steeples, 
house-tops, and other elevated places, gave considerably less rain 
than if they were on the ground, and it has very recently been 
shown that the variation is most rapid in the close neighbourhood 
of the ground. All kinds of theories have been started to explain 
this phenomenon ; but I have attempted to show that it is simply 
due to the interference of wind which deflects more or less rain 
from all the gauges which are at all exposed to it. 

^^ The great magnetic power of iron renders it a constant 
source of disturbance in all magnetic experiments. ... In 
some cases, magnetic observations have been seriously disturbed 
by the existence of masses of iron in the neighbourhood. In 
Faraday's experiments upon feebly magnetic or diamagnetic 
substances, he took the greatest precautions against the presence 
of any disturbing substance in the copper wire, wax, paper, and 
other articles used in suspending the test objects. It was his in- 
variable custom to try the effect of the magnet upon the appara- 
tus in the absence of the object of experiment, and without this 
preliminary trial no confidence could be placed in the results."^ 

It is sometimes impossible to remove the suspected cause 
experimentally without materially changing the attendant 
circumstances; or it may be impossible to remove it at all, as in 
the case of gravity. But this difficulty may often be over- 
come by introducing a circumstance which overcomes or 
neutralizes the effect of the supposed cause without altering the 
rest of the phenomena. Thus, e,g.^ the rain gauges placed in 
elevated positions which were mentioned above, might be 
protected from the wind by screening. The effect of this 
disturbing element would thus be neutralized, leaving it 
possible to observe what results, if any, in the quantity of 
rainfall followed a change of elevation. 

^ Jevons, op. cit., pp. 40, 41. 



CHAPTER XVII 

DETERMINATION OF CAUSAL RELATIONS {continued) 

§ 6i. The Joint Method of Agreement and Difference. — 

The method of Difference can be apphed only when all 
concomitant circumstances, except one, remain constant. In 
order to apply this method, then, it is necessary either to 
find two instances which differ only in a single circumstance, 
or to proceed by means of experiments, adding or removing 
a single circumstance at a time and noting the result. The 
difficulty is to find instances that differ only in a single 
circumstance in fields where, from the nature of the case, 
experiments cannot be used. For example, in trying to 
reach generalizations regarding the behaviour of human 
individuals or human societies — in looking for moral, or so- 
cial, or economic laws — it is, of course, impossible to em- 
ploy experiment. Nor, when dealing with individuals and 
societies, can we find two instances which certainly differ 
from each other in only a single circumstance. In studying 
phenomena of this kind, then, it is necessary to employ an- 
other method as an instrument of analysis. What is done 
by this new method is to take a number of instances instead 
of only two. A number of instances where the phenomenon 
to be investigated occurs are compared together, and like- 
wise a number of instances where it does not occur, and 
the results of the two comparisons noted. 

This is really to combine the principle of the method of Agree- 
ment with that of the method of Difference. Mill, accordingly, 

249 



250 Determination of Causal Relations 

has called this the Joint Method of Agreement and Dif- 
ference, and has given the following statement of its canon: — 
/ ^' If two or more instances in which the phenomenon occurs have 
I only one circumstance in common ^ while two or more instances in 
j which it does not occur have nothing in common save the absence 
>L of that circumstance J the circumstance in which alone the two 
I sets of instances differ is the effect, or the cause, or an indis- 
KpensaUe part of the cause, of the phenomenon,^' By the help 
of this method, the weakness which has already been noticed 
in the method of Agreement is overcome. We first compare 
different instances in which the phenomenon occurs. If 
these are found to agree in only a single circumstance, we 
conclude, according to the canon of Agreement, that this cir- 
cumstance is probably connected causally with the phe- 
nomenon in which we are interested. But the proof is not 
yet complete. To really prove the connection, we must 
show that wherever the circumstance is absent, there the 
phenomenon is also absent. 

In interpreting this canon, it is important to remember 
that both positive and negative instances must be selected 
from the field within which our previous knowledge enables 
us to say that the cause (or effect) sought for is to be found. 
The purpose of the instances, as has been frequently pointed 
out, is to bring to our attention circumstances which might 
conceivably make a difference. It is, of course, impossible 
. to predict in advance all the things that might make a differ- 
ence; but the possibilities fall within a more or less definite 
range. In both the positive and negative set of instances, 
then, we are concerned only with circumstances that might 
be relevant. The negative instances to be chosen are there- 
fore, not any cases ^ where the phenomenon does not appear,' 



§ 6i. Joint Method of Agreement and Dijference 251 

but where, in addition, circumstances which were previously 
found in conjunction with the phenomenon, and which might 
have been supposed to be causally connected with it, are now 
shown to be sometimes, at least, present when it is absent. 
To represent the working of the matter schematically, we 
may analyze the instances where the phenomenon, P, occurs 
into the following circumstances : — 

Instance i a, 5, ^, ^, ^. 

Instance 2 . /, c, a, ^, ^. 

Instance 3 d^ m, hj c, e. 

Instance 4 k, n, c, g, a. 

The method of Agreement, in such a case, would lead to the 
conclusion that c is probably connected causally with P. 
To strengthen and render more definite that conclusion, 
however, the Joint method introduces the comparison of 
instances, as much like the former group as possible and 
known to exhibit at least many of the same circumstances, 
but where the phenomenon in question does not occur. These 
instances of the absence of P would then be represented 
thus: — 

Instance i bj k, n, g, a. 

Instance 2 . d, e, b, m, f. 

Instance 3 k, I, s, g, b. 

Instance 4 Xj e, n, a, f. 

What is of significance in this latter series is not merely that 
the instances show nothing common except the absence of P, 
but that the same ' circumstances ' excluded by the former 
analysis are now seen to exist in the absence of that phenom- 
enon. But what may be present when a phenomenon is 
absent is not its cause or effect. All these possible circum- 



252 Determination of Causal Relations 

stances, then, a, 6, J, etc., are again eliminated by the com- 
parison of negative instances, leaving as before c as that 
which is causally connected with P. 

The canon of this method, then, as stated by Mill must be 
read with these restrictions in mind. The actual working of 
the method is better described in the following words: 
If when two sets of instances — one in which the phenome- 
non under investigation is present and one in which it is 
absent — are drawn from the same field of inquiry ^ it is found 
that there is one circumstance which is invariably present 
when the phenomenon occurs and invariably absent when it 
does not occur, while each of the other circumstances is both 
sometimes absent when the phenomenon is present, and some- 
times present when it is absent, then the first circumstance is 
causally connected with the phenomenon. 

As an illustration of the method of Agreement and Difference 
the following instance will serve: — 

We may suppose that in a certain part of the country it 
was noticed that a considerable difference existed in the 
number of criminal offences committed, in proportion to 
the number of inhabitants, in the various towns. In several 
towns the percentage was high, while in others it was rela- 
tively small. This being so, a question naturally arose as 
to the cause of the high percentage. Now there were among 
the people various opinions concerning the matter. One 
thought it was due to the small number of police, a second 
believed it was caused by the inefficiency of the public 
schools, a third attributed it to the inadequacy of the penal- 
ties attached to the violation of law, a fourth was convinced 
that it was due to lack of activity on the part of the churches, 
while a fifth insisted that the phenomenon could be accounted 



§ 6i. Joint Method of Agreement and Dijference 253 

for by the presence of licensed saloons. Not being able to 
agree about the matter, it was decided to appoint a commit- 
tee to investigate the circumstances existing in variou towns 
where the same general conditions prevailed, and upon the 
basis of this comparison to decide the matter. The towns 
with a high criminal percentage were examined first. The 
report of conditions there was as follows: — 

Town A : Small police force — efficient schools — severe 

penalties — inactive churches — licensed saloons. 
Town B : Small police force — efficient schools — light 

penalties — active churches — licensed saloons. 
Town C : Large police force — inefficient schools — severe 

penalties — active churches — licensed saloons. 
Town D : Large police force — inefficient schools — light 

penalties — inactive churches — licensed saloons. 

This report revealed the fact that in each of these towns 
having a high criminal percentage there was one circumstance, 
and only one, invariably present, — the licensed saloon. This 
rendered it probable that the saloon was the cause of the high 
percentage of crime. Still, before finally deciding, it was 
thought well to investigate negative instances as well; that is, 
towns in which the high percentage of crime did not occur. 
The report of conditions there was as follows: — 

Town E : Large police force — efficient schools — severe 
penalties — active churches — no licensed saloons. 

Town F : Large police force — inefficient schools — light 
penalties — active churches — no licensed saloons. 

Town G : Small police force — efficient schools — light 
penalties — inactive churches — no licensed saloons. 



254 Determination of Causal Relations 

Town H : Small police force — inefficient schools — severe 
penalties — active churches — no licensed saloons. 

This table showed that in the absence of the phenomenon 
(high criminal percentage) one and only one of the condi- 
tions concerned was invariably absent; namely, the licensed 
saloon. This confirmed the previous report and established 
to the satisfaction of all that the saloon was, at least, the 
main cause of the high criminal percentage in the cities 
concerned. 

Of course, it is obvious that this can be no more than a hypothet- 
ical case. In actual life, the conditions of the method would never 
be so exactly realized. In the first place, in any such investigation, 
it would probably never be possible to find instances where one con- 
dition is invariably present when the phenomenon occurs, and 
invariably absent when it does not occur, as the illustration supposes. 
We could, at most, expect that one condition would exhibit a 
tendency to be present when the phenomenon occurs and absent 
when it does not occur. That is, there might well be instances 
met with in which a combination of other conditions might render 
unnecessary the presence of the usually essential one. In the 
second place, it would not be satisfactory in actual life to deal with 
such vague terms as ^efficient' schools, or ^active' churches. On 
the contrary, we should, in a careful investigation, resort to statistics 
in order to secure greater definiteness and accuracy. The compar- 
ative number of the churches, the size of the police force, the 
number of saloons, would be noted and compared with the per- 
centage of crime in order if possible to determine which of the 
above-mentioned circumstances is causally connected with the 
large number of criminals. That is, although we should not be 
likely to find fulfilled the strict requirements which this method 
makes, we should strengthen the inference by showing that 



§ 62. The Method of Concomitant Vmiations 255 

definite quantitative relations exist, as indicated by the statistics, 
between certain of the circumstances in question. 

It is usual to speak of this method as that to which recourse 
must be had when it is impossible to employ experiment. As a 
matter of fact, this illustration seems to show that the strict require- 
ments of the method can never be realized except where experi- 
ment can be employed to isolate and control the conditions. In 
fields where this is impossible, it is necessary, as we have seen, to 
employ statistics as an instrument of analysis. Where the method 
is not supplemented by determining the relation of the various in- 
stances experimentally, or by making possible exact comparisons 
through the use of statistics, it can yield only vague and unsatis- 
factory results. It is obvious, therefore, that the various methods 
must continually supplement one another in actual operation if the 
complex and changing conditions of experience are to be success- 
fully dealt with at all. 

§ 62. The Method of Concomitant Variations. — The 
methods of Agreement and Difference are employed, as we 
have seen, to determine what events are necessarily con- 
nected as causes and effects. By examining a considerable 
number of instances, and by comparing the cases in which 
the phenomenon of interest to us occurs, with cases in which 
it does not occur, we seek to rule out all accidental and un- 
essential conjunctions, and thus to determine the true law 
of causal connection. But the discovery of certain forms of 
agreement or correspondence in the variations of phenomena, 
or groups of phenomena, often enables us to detect a causal 
relation between them (cf. pp. 221-223). The variations or 
changing states of all phenomena are events in time. Now, 
when it is observed that certain of these events continue to 
show correspondences throughout a series of variations, it 
is inferred that the conjunction is not accidental, but indi- 



256 Determination of Causal Relations 

cates the existence of a causal connection. This correla- 
tion of events may be discovered through correspondences 
in temporal or spatial arrangement of phenomena, in their 
progression, or in changes of quality or quantity. ^The dis- 
covery of concomitant variations, however, is of importance 
in science, not merely because it assists us in determining 
what events are related as causes and effects, but also be- 
cause the exact form of the causal relation can thereby be 
rendered more definite and satisfactory, j For scientific 
knowledge the discovery of a ^ general correspondence ' be- 
tween certain phenomena is not enough; it is necessary to 
obtain some exact expression of the relation between the two 
sets of variations. This is found by reducing the variations 
to terms of quantity through the application of a common 
unit of measurement. The law or ratio of the variations 
may then be expressed in numerical terms. Now the 
scientist tries to include in his statement of causal laws, 
whenever possible, precise information regarding the quanti- 
tative relations of the phenomena concerned. Indeed, we 
may almost say that science does not exist until the quanti- 
tative aspects of phenomena are taken into account — until 
things are weighed and measured. The physicist does not 
think his work finished when he has proved that sound is 
produced by atmospheric vibrations. He carries on his 
analysis until he can discover the quantitative relations be- 
tween the amplitude and velocity of the vibrations, and the 
loudness and pitch of the resulting tone. And the psycholo- 
gist is not satisfied with the general statement that certain 
sensations are causally connected with certain kinds of stim- 
uli; but he seeks to discover, whenever possible, the exact 
quantitative relation between sensation and stimulus. In 



§ 62. The Method of Concomitant Variations 257 

short, the most important feature, the very essence, one 
may say, of modern scientific investigation, is the estabhsh- 
ment of quantitative relations. 

Looking at two things with respect to the order and pro- 
gression exhibited by their manner of appearance, then, we 
say that when their variations keep pace with each other, 
they are in some way causally connected. What it is neces- 
sary to establish, in order to justify the inference to causal 
relationship, is that there is some definitely expressible rela- 
tionship between the changes shown by the two series. ' Noth- 
ing is the cause of a phenomenon that varies when the latter 
is constant, or is constant when it varies; or between whose 
changes and that of the phenomenon there is not some 
correspondence.' It is not necessary, however, that the va- 
riations shown by the two series should always be in the same 
direction. One series, for example, may increase as the 
other increases, or the two series of changes may be in in- 
verse ratio. The essential requirement is that there shall be 
some definite relationship clearly made out between the two 
series of events. 

The following is Mill's statement of the canon: ^^ Whatever 
"phenomenon varies in any manner whenever another phenome- 
non varies in some particular manner^ is either a cause or an 
effect of that phenomenon^ or is connected with it through 
some fact of causation,'^' The illustrations of this law given 
by Jevons are so pertinent that we cannot do better than 
adopt them: — 

*'The illustrations of this law are infinitely numerous. Thus 
Mr. Joule, of Manchester, conclusively proved that friction is a cause 
of heat by expending exact quantities of force by rubbing one sub- 
stance against another, and showed that the heat produced was 



2c;8 Determination of Causal Relations 

exactly greater or less in proportion as the force was greater or less. 
We can apply the method to many cases which had previously been 
treated by the simple method of difference ; thus instead of striking 
a bell in a complete vacuum, we can strike it with a very little air in 
the receiver of the air-pump, and we then hear a very faint sound 
which increases or decreases every time we increase or diminish the 
density of the air. This experiment conclusively satisfies any per- 
son that air is the cause of the transmission of sound. 

*^It is this method which often enables us to detect the material 
connection which exists between two bodies. For a long time it 
had been doubtful whether the red flames seen in total eclipses of 
the sun belonged to the sun or moon ; but during the last eclipse of 
the sun, it was noticed that the flames moved with the sun, and were 
graduafly covered and uncovered by the moon at successive in- 
stants of the eclipse. No one could doubt thenceforth that they 
belonged to the sun. 

'^Whenever, again, phenomena go through Periodic Changes, 
alternately increasing and decreasing, we should seek for other phe- 
nomena which go through changes in exactly the same periods, and 
these will probably be a connection of cause and effect. It is thus 
that the tides are proved to be due to the attraction of the moon and 
sun, because the periods of high and low, spring and neap tides, 
succeed each other in intervals corresponding to the apparent revo- 
lutions of those bodies round the earth. The fact that the moon 
revolves upon its own axis in exactly the same period that it revolves 
round the earth, so that for unknown ages past the sam.e side of the 
moon has always been turned toward the earth, is a most perfect 
case of concomitant variations, conclusively proving that the earth's 
attraction governs the motions of the moon on its own axis. 

''The most extraordinary case of variations, however, consists in 
the connection which has of late years been shown to exist between 
the Aurora Borealis, magnetic storms, and the spots on the sun. 
It has only in the last thirty or forty years become known that the 



§ 62. The Method of Concomitant Variations 259 

magnetic compass is subject at intervals to very slight, but curious, 
movements ; and that, at the same time, there are usually natural 
currents of electricity produced in telegraph wires, so as to interfere 
with the transmission of messages. These disturbances are known 
as magnetic storms, and are often observed to occur when a fine dis- 
play of the Northern or Southern Lights is taking place in some 
part of the earth. Observations during many years have shown 
that these storms come to their worst at the end of every eleven 
years. . . . Close observations of the sun during thirty or forty 
years have shown that the size and number of the dark spots, which 
are gigantic storms going on upon the sun's surface, increase and 
decrease exactly at the same periods of time as the magnetic storms 
upon the earth's surface. No one can doubt, then, that these strange 
phenomena are connected together, though the mode of the con- 
nection is quite unknown. . . . This is a most remarkable and 
extensive case, of concomitant variations. " ^ 

(i) In employing this method it is, of course, hazardous to infer 
the existence of a universal law of correlation without examining in 
some detail the nature of the concomitant variations. In general 
the more definitely the relationship can be shown in a consider- 
able number of cases, the more ground there is for the conclusion 
that the conjunction is not accidental. Moreover, it is also neces- 
sary that observations should be extended over a considerable range 
in order to determine whether the supposed law of correlation has 
any limits, and if so how they are to be defined. For example, in 
Weber's law we have an exact expression for the correlation of the 
quantity of the stimulus in the case of the various sense organs 
and the intensity of the resulting sensation. But in every case this 
exact correlation of stimulus and sensation has an upper and lower 
limit, beyondwhichit either changes its character or ceases altogether. 

(2) The close and almost inseparable connection of the different 
methods in actual use, which was emphasized in the preceding sec- 
^ Jevons, Lessons in Logic, pp. 249-251. 



26o Determination of Causal Relations 

tion, is also here clearly evident. In many fields it is only through ex- 
periment that the fact of correspondences between phenomena can 
be brought to light, and the character and law of their correlations 
exactly determined. But to introduce experiment for these pur- 
poses is, of course, to supplement the method of Concomitant Vari- 
ations by the method of Difference. Similarly, in performing experi- 
ments where it is impossible to withdraw a certain element, and 
thus by comparison to note what its cause or effect is, as 
the strict canon of Difference requires, we may be able to isolate 
the element practically by causing it to vary while other circum- 
stances are kept constant. It is then possible to note the variations 
in the corresponding series and thus to determine what is causally 
correlated with the element in question. Foi example, if the prob- 
lem were to determine the effect of moisture on growing plants 
it would, of course, be impossible to elimin^ te moisture entirely with- 
out killing the plant and putting an end to the experiraent. But by 
varying the amount of moisture, and noting concomitant changes 
in the plant, both methods of analysis are combined. 

§ 63. The Method of Residues. — We have said that 
modern science employs measurement whenever possible, 
in order to determine exactly the quantitative relations of 
phenomena. Groups of facts whose connections are at first 
not perceived, or at best but vaguely apprehended, are 
brought into close relations with one another by the estab- 
lishment of definite quantitative relations. The knowledge 
that electricity possesses energy, for example, is very vague 
and incomplete when compared with the definite equations 
which the physicist can furnish between the electrical cur- 
rent generated under certain definite conditions, and the 
amount of work which it is capable of performing. But the 
discovery of quantitative relations not only renders our 
knowledge more perfect and complete, it also enables us in 



§ 63. The Method of Residues 261 

some cases to detect laws of connection which would not 
otherwise be observed. We have already seen how the per- 
ception of corresponding changes in the quantities of phe- 
nomena has led to the discovery of causal laws by means 
of the method of Concomitant Variations. The method of 
Residues, which we now have to discuss, is also largely 
dependent on quantitative determination. 

In general, this method calls attention to any remainder 
or residue which is left over after other portions of a complex 
phenomenon have been explained. There are two results 
of this method which may be discussed separately. 

{a) The application of this method to a complex phenom- 
enon which is the result of several causes, often enables us 
to determine what part each of these causes plays in the 
determination of the whole fact under consideration. Mill's 
fifth canon seems to apply to this case. It is as follows: 
Subduct from any phenomenon such part as is known by pre- 
vious inductions to be the effect of certain antecedents, and the 
residue of the phenomenon is the effect of the remaining ante- 
cedents. Thus, if it is known that the complex phenomenon 
BAC is the result of bac, and if it is further known that a is 
the cause of A, and b of B, it follows, of course, by sub- 
traction that the residue still unexplained, C, is caused by 
c, the remaining antecedent. 

Of course the application of this method in concrete cases does 
not usually resolve itself into such a simple process of subtraction. 
It requires work — ^previous inductions,' as Mill says — to deter- 
mine what are the whole number of antecedents in any case, as well 
as to isolate the various antecedents so as to determine exactly what 
part of the effect is to be ascribed to each one. This may be illus- 
trated by an example : after my student's lamp has been lighted two 



262 Determination of Causal Relations 

hours, I find the thermometer has risen from 65° to 70° Fahr. The 
phenomenon to be explained then is the additional 5° of heat. 
There is no fire, and it seems that the increase in temperature must 
be due to the lamp, and the heat given off from my body during 
this period. Suppose that the lamp is burned for the same length 
of time while the room is unoccupied, all other conditions remaining 
the same, and that the thermometer shows an increase of 4° in the 
temperature. By subtraction we could conclude that the heat given 
off by the body on the former occasion was the cause of the addi- 
tional degree of temperature. 

To carry the process of analysis a step further. Let us suppose 
that a half pint of oil, which is composed of hydrogen and carbon, 
has been consumed. We could determine, by measuring the heat 
produced by the oxidation of the exact amount of carbon contained 
in one-half a pint of oil, what quantity of heat is due to the com- 
bustion of the carbon contained in the oil, and, by subtraction, 
what must be ascribed to the burning of the hydrogen.^ 

(&) The second case in which this method may be applied 
is where there is an unexplained remainder or residue left 
over after the result of all the known causes has been calcu- 
lated. Mill does not distinguish between such instances 
and the method of simple subtraction discussed above. 
Since, however, the cause must explain the whole of the 
effect, the method of residues enjoins us to continue the search 
for explanation. When any part of a complex phenomenon 
is still unexplained by the causes which have been assigned, a 
further cause for this remainder must he sought. If, for ex- 
ample, it were found by actual measurement that the heat 
produced by the lamp, and by the body of the occupant, were 

^ This is, of course, not strictly correct, for it leaves out of account the 
heat generated by the chemical combination of the carbon and hydrogen. 
It may, therefore, serve to illustrate a case where the method of Residues 
breaks down. 



§ 63. The Method of Residues 263 

not sufficient to account for the change in temperature of the 
room, it would be necessary to seek for some further cause 
to account for this unexpected remainder. 

This method can scarcely be said to be more than a de- 
mand for complete and precise explanation. The attempt, 
however, to account for unexplained residues has led to 
many extremely important discoveries in science. Residual 
phenomena are often so obscure, and appear so uninterest- 
ing and unimportant to the ordinary mind, that they are 
passed over without explanation. It usually requires the 
eye of a scientific genius to see the importance of things 
which appear trivial and unessential. With Darwin, facts 
which might appear to an ordinary observer mere unimpor- 
tant exceptions, were made the object of special attention, 
and often served as starting-points for his investigations. 
Francis Darwin, speaking of his father, says: ''There was 
one quality of mind which seemed to be of special and ex- 
treme advantage in leading him to make discoveries. It 
was the power of never letting exceptions pass unnoticed. 
. . . A point apparently slight and unconnected with his 
present work is passed over by many a man almost uncon- 
sciously, with some half-considered explanation, which is 
really no explanation. It was just these things that he 
seized upon to make a start." ^ 

Among the many important discoveries which have resulted from 
the investigation of some obscure and seemingly unimportant fact, 
we may mention that of ozone. It had been observed for a long 
time that the passage of electric sparks through the air is accom- 
panied by a peculiar odour. This odour was also found near 
electrical machines, and was known as the 'electrical smell.' No 
"^ Life and Letters of Charles Darwin^ Vol. I., p. 125. 



264 Detennination of Causal Relations 

one seemed to have attached any importance to it or to have at- 
tempted to explain it in any way, until Friedrich Schonbein, a pro- 
fessor of chemistry at Basel, turned his attention to the subject. 
The result of his investigations was the discovery of ozone, the 
peculiar modification of oxygen, which was the cause of the odour. 
Another very striking example of the application of this method 
is afforded by the history of the discovery of the planet Neptune. 
In 1781 a new planet was discovered moving outside all the other 
planets by Sir William Herschel. This was the planet Uranus. 
When its orbit came to be calculated, it was found that it did not 
move as it might be expected to do according to the theory of gravi- 
tation. That is, the attraction of the sun and the known planets did 
not account for the path it took: it moved outwards into space 
farther than it ought to have done. It was evident that either some 
mistake must have been made in the observation of the astronomers, 
or some unknown body must be dragging it out of its course. No 
traces of any such planet could be perceived, and the problem 
remained unsolved. In 1843, ^ student of St. John's College, 
Cambridge, named Adams, undertook to work out the movements 
of Uranus, to discover, if possible, the position of the body which 
was pulling it out of what would otherwise be its proper path, the 
attractions exercised by the sun and the planets in their different 
positions, and to show what effect they would have in determining 
the orbit of Uranus. Whenever the planet was deflected outwards, 
it was necessary to show where the body was situated which was 
thus influencing it. In 1845 ^^ was able to send a paper to the 
astronomer royal at Greenwich, informing him in what quarter of 
the heavens the new planet should be observed. When the discov- 
ery was afterwards made, it was proved that his calculations were 
almost exactly correct. A failure on the part of the astronomer 
royal to cooperate by looking through his telescope for the planet 
gave the prior right of discovery to a Frenchman named Leverrier. 
The latter worked out his calculations in the same way as Adams, 



§ 63. The Method of Residues 265 

and obtained almost exactly the same results. He sent these results 
to Professor Galle of the Berlin University on the 23d September, 
1864, asking him to look in the part of the heavens which he 
indicated. That same evening, by following out the directions, the 
planet was discovered in almost the exact spot predicted.^ 

The history of this discovery illustrates as well several methods 
and processes which we have not yet discussed, such as the forma- 
tion and verification of hypotheses. It is also interesting as showing 
how reason is able, under certain conditions, to anticipate per- 
ception. The relations and forces of the heavenly bodies had 
been so perfectly formulated in the law of gravitation that these 
two investigators, working in their studies, were able to predict 
not only the presence, but the exact position of a planet which up 
to that time had never been observed. It is where mathematical 
methods can be used that such anticipation is most often possible. 
Hence this use of the method of Residues has frequently led to 
important results in astronomy. 

REFERENCES TO CHAPTERS XV. AND XVI. 

Mill, Logic, Bk. III., Chs. VIII. and IX. 

Joseph, An Introduction to Logic, Ch. XX. 

Sigwart, Logic, Vol. II., § 95. 

Hobhouse, The Theory of Knowledge, Chs. XIII.-XV. 

^ Cf. Gierke, A Popular History of Astronomy during the Nineteenth 
Century, pp. 96 ff. ; Buckley, A Short History of Natural Science, pp. 302 £f. 



CHAPTER XVIII 

ANALOGY 

§ 64. Explanation by Analogy. — An 'Analogy' may be 
defined in general terms as an agreement, resemblance, or 
proportion between the relations of things to one another, or 
between the things themselves. Thus it might be said that 
there is an analogy between the relations of a ruler to his 
people and those of the captain of a vessel to members of his 
crew. Or an analogy might be said to exist simply between 
a ruler and a captain, or between a state and a ship. In logic, 
analogy is used more specifically as a form of reasoning in 
which, from the resemblances of two or more things in certain 
respects, their likeness in other respects is inferred. 

The tendency to note resemblances and to assume that 
things alike in certain respects are alike in all, is present from 
the first in all stages of thinking. We have seen (§ 50) that 
this principle guides inductive inquiry by furnishing sugges- 
tions as to what may be expected when new facts and condi- 
tions are met with. But in noting, in our earlier discussion, 
the operation of this principle, no detailed description of its 
principles was given, or any adequate account of the part it 
plays in organizing experience. In this chapter emphasis is 
laid more particularly on the function that Analogy performs 
at a somewhat advanced stage of inductive inquiry, in leading 
on to the higher generalizations of science. At a lower level 

the connections and relations suggested by Analogy are of a 

266 



§ 64. Explanation by Analogy 267 

factual and descriptive character. For example, Analogy 
might suggest in a particular case that the severe frost is the 
cause of the bursting of water pipes, without affording any 
clear understanding of the universal law through which these 
things are connected. In more advanced stages of know- 
ledge, however, Analogy is used consciously and critically as 
a means of deriving general laws and principles of explana- 
tion. In proceeding to the discussion of this more gcxplicit 
use of Analogy, we may then be said to be passing from 
Description to Explanation. But, as has already been 
pointed out (§§ 52, 53), no hard and fast line can be drawn 
between the determination of the nature and connection of 
facts, and their explanation. The task which our thought 
is called upon to perform is to transform obscurely known 
and isolated facts into an orderly and consistent system of 
knowledge, and this process is continuous throughout. But, 
keeping this in mind, one may still say that it is necessary, 
in the first place, for the facts to be thoroughly analyzed and 
carefully examined; and, secondly, for them to be grouped 
together according to some general principle or principles 
which shall make clear and intelligible the relations in which 
they stand to one another. 

To explain is just to show that some fact or group of facts 
is related to some other fact or group with which we are ac- 
quainted. So far as the methods we have discussed enable us 
to establish connections between events, they may fairly 
claim to be methods of explanation. Nevertheless, although 
the difference between these methods, and those of explanation 
in terms of wider generalizations, is one of degree rather than 
of essential nature, it is important to keep it in mind. The 
canons which were stated in the last two chapters — what 



268 Analogy 

Mill named the experimental methods — are rules for deter- 
mining causal connections between phenomena. The prob- 
lem in those chapters was to determine vv^hat particular 
phenomena of our experience are essentially and necessarily 
connected as antecedents and consequents. This constitutes 
a more or less distinct step in the work of systematization 
which is carried on by thought. The method of Difference, 
for instance, enables us to say that hot water will break thick 
glasses when poured into them, but will not damage thin 
ones. ^ So much for the fact^ we say, ^ but the explanation is 
still wanting.' We must try to make the fact intelligible by 
going outside of it, and showing that this behaviour on the 
part of the glasses is simply a case or illustration of what we 
already know of the properties of bodies when heated. 
Again, the method of Concomitant Variations, as we have seen 
from Jevons's example, has led us to believe in some causal 
connection between electrical storms, sun-spots, and the 
Aurora Borealis. In this instance, knowledge has not been 
able to advance beyond the fact to its explanation. No satis- 
factory theory has yet been established to account for the un- 
doubted fact that these phenomena are in some way causally 
connected. 

The principle of Analogy is resemblance. The phenome- 
non to be explained is connected with some more familiar 
occurrence through a perceived or imagined likeness between 
the two cases. All our first rude classifications and explana- 
tions are based on this principle. In the early stages of the 
history of the race, everything was explained on the analogy of 
human actions (cf. § 89). All natural events, that is, were 
supposed to be produced by superhuman agents, who were, 
however, endowed with essentially the same qualities as man. 



§ 64. Explanation by Analogy 269 

In the thunder, the men of a primitive age heard the voice 
of a god. An echpse of the sun or moon was interpreted as 
a divine sign or warning. When the sea became tempestuous 
and lashed its shores, they beheved that the sea-god was angry. 
In every case, they interpreted these mysterious happenings 
of nature by referring them to causes similar in character to 
those which they best understood as effective forces — the 
motives and vohtions of themselves and their fellows. 

The principle of analogy is employed in the same way in 
modern times. It is true that we no longer think that natural 
events are directly caused by the action of some spiritual agent 
more or less like ourselves. But, when we endeavour to show 
that the phenomena which we are interested to explain are 
similar in important respects to some group of facts with 
whose mode of operation we are familiar, we proceed by 
analogy. On the basis of this similarity, we argue that the 
phenomena with which we are dealing probably have the 
same properties, or operate in the same way, or are governed 
by the same laws, as the better-known facts which they re- 
semble. The formula of analogy may be stated in this way: 
Two things resemble each other in one or more respects, they 
are therefore of the same general type or character; it follows 
that a certain proposition which is true of the one is prob- 
ably true of the other. The following example of analogy 
has been frequently used as an illustration : — 

^^We may observe a very great similitude between this earth 
which we inhabit, and the other planets, Saturn, Jupiter, Mars, 
Venus, and Mercury. They all revolve round the sun, as the earth 
does, alt-hough at different distances and in different periods. They 
borrow all their light from the sun, as the earth does. Several of 
them are known to revolve around their axes like the earth, and by 



2/0 Analogy 

that means must have a like succession of day and night. Some of 
them have moons that serve to give them light in the absence of the 
sun, as our moon does to us. They are all in their motions subject 
to the same law of gravitation as the earth is. From all this simili- 
tude, it is not unreasonable to think that those planets may, like 
our earth, be the habitation of various orders of living creatures. " ^ 
The word ^analogy' at the present time is somewhat loosely 
used for any mark of similarity or resemblance which enables us 
to reason from one thing to another. As already noted, the term 
is also applied either to a likeness between two things, or a likeness 
between certain relations of things. In the latter case, there is of 
course a proportion expressed, as when it is said that the relation 
of a clergyman to his parishioners is analogous to that of a physi- 
cian to his patients. The purpose of such comparisons is to 
afford a basis for inferring that the rights or duties that exist in 
the one case obtain also in the other. In such cases, however, 
we have always to ask if there are not differences, as well as 
likenesses, in the two sets of relations. This employment of 
analogy is more strictly that which was noted and defined by 
Aristotle. ^^The original word dmXoyta, as employed by Aris- 
totle, corresponds to the word Proportion in Arithmetic; it signi- 
fies an equality of ratios, lo-6Tr]<i Xoywi/ : two compared with four is 
analogous to four compared with eight. There is something of 
the same meaning in the technical use of the word in physiology, 
where it is used to signify similarity of function as distinguished 
from similarity of structure, which is called homology; thus the tail 
of a whale is analogous to the tail of a fish, inasmuch as it is simi- 
larly used for motion, but is homologous with the hind legs of a 
quadruped. A man's arms are homologous with a horse's fore 
legs, but they are not analogous, inasmuch as they are not used for 
progression."^ 

^ Reid, Intellectual Powers of Man^ Essay I., Ch. III. 
2 Minto, Logic, Inductive and Deductive, p. 367. 



§ 65. Analogy and Explanatory Hypotheses 27 1 

Apart from these technical uses, what is known as analogical 
reasoning may, perhaps, be best defined as an argument from 
similar instances. In analogy, we do not stop to work out a 
law of connection between phenomena by comparing a 
number of cases, or by using any of the ordinary inductive 
canons. But finding a striking resemblance between some 
circumstance — relation, quality, arrangement, function, etc. 
— in the phenomena to be explained, and some phenomena 
with which we are already acquainted, we use the latter as 
a basis for conclusions about the former. Analogy is thus 
an argument from examples or instances, its value depending 
upon the real identity in some important aspect of the cases 
compared. When, however, our thought is able to extend to 
a new case, or set of cases, some general law or principle 
with whose operation it is already acquainted in other in- 
stances, we have passed beyond analogy to a higher form of 
explanation. In the former case, we argue from the resem- 
blance of instances; in the latter, the thread which binds 
the new instance with the old is the identity of a general 
principle. 

§ 65. Analogy as Suggestive of Explanatory Hypotheses. 
— We have shown above that analogical reasoning depends on 
the resemblance which exists between individual cases or 
instances, and that it does not itself succeed in formulating 
any general law or principle. The next section will show 
in more detail in what respects the principle of analogy falls 
short, and why, taken by itself, it can only be regarded as 
incomplete explanation. Here we have to notice the im- 
portant part which it plays in suggesting laws and principles. 
Although analogy ^ sticks in the particular instances,' it leads 
the mind on to general laws and explanatory theories. It is 



2/2 Afialogy 

thus of the greatest importance as a necessary stage on the 
way to complete explanation. 

When we are able to discover some general resemblance 
between a group of phenomena which we are interested to 
explain, and another group whose principle of operation we 
already understand, our thought strives to extend the known 
principle and to bring the new facts under it. The unknown 
or unexplained facts are thus brought under a known law. It 
is of course true that the application of the law to a new set of 
facts broadens our conception of its scope, and often requires 
us to state it in a more adequate way. Thus the analogy 
which Newton perceived between the heavenly bodies falling 
through space and the falling of the apple towards the ground, 
led to the formulation in exact mathematical terms of the 
universal law of gravitation. Our knowledge of the various 
functions of plants — digestion, reproduction, etc. — has 
been obtained by ascribing to the various organs of the plant, 
purposes analogous to those which are fulfilled by the parts 
of animal bodies. And, in turn, the study of plant physiology 
has thrown light upon animal physiology, and enlarged and 
modified many of its theories. Again, the explanation of 
many geological changes, — the wearing away of rocks, the 
formation of deltas or of great ravines, of vegetable mould, 
etc., — is facilitated by a discovery of their analogy with 
familiar events which happen constantly before our eyes. 

An extremely interesting instance of the part which analogy 
plays in suggesting possible explanations, is found in the account 
of the discovery of the principle of Natural Selection given by Dar- 
win in his Autobiography. In 1837 Darwin opened a note-book 
for the purpose of recording all facts in any way connected with the 
variation of species in nature and under domestication. He first 



§ 65. Analogy and Explanatory Hypotheses 273 

investigated the variations of plants and animals v^hich are produced 
under domestication, by printed inquiries, by conversation with 
skilful breeders, and by extensive reading. ' ' I soon found, " he says, 
"that selection was the keystone of man's success in making useful 
races of plants and animals. " When useful or pleasing varieties 
of plants or animals occur, the gardener or breeder preserves them, 
and their peculiar qualities are transmitted to their offspring. And, 
in a number of generations, these qualities become more pronounced 
through accumulation. The differences between varieties of the 
same species of domesticated animals — varieties which are as differ- 
ent, for example, as the mastiff and Skye terrier — are due to the 
selective agency of man. But is there anything analogous takes 
place on an indefinitely larger scale in nature? If so, what is it 
which plays the part of the gardener or breeder, and preserves 
certain varieties ? 

When Darwin had reached this point in his investigations, and, 
had come to appreciate what selection could do, he happened to 
read Malthus's book. On Population. The purpose of this book 
was to dispel the optimistic ideas of some of the writers of the 
eighteenth century who looked for the speedy realization of social 
well-being and happiness. Such an ideal is impossible of fulfilment, 
said Malthus, because of the inevitable tendency of population to 
increase faster than the supply of food. Human beings increase in 
a geometrical ratio ; the means of subsistence, at best, only by an 
arithmetical ratio. The population will thus constantly tend to 
exceed the limit of the food supply, and will be kept in check only 
by starvation. A constant struggle for food is the lot, then, to 
which each individual is doomed in virtue of this law. Darwin's 
observations of the rate at which plants and animals tend to repro- 
duce their kind, led him at once to extend Malthus's principle to 
the whole of nature. The fecundity of natural beings leads to a 
struggle for existence, not merely among men, but throughout the 
whole organic world. And if there is a struggle, we have natural 



2/4 Analogy 

selection or the survival of the fittest. Darwin saw ^'that natural 
selection was the inevitable result of the rapid increase of all organic 
beings. " It is not difficult to see that this discovery was the result 
of Darwin's wonderful power of perceiving analogies between differ- 
ent classes of facts. His genius led him to recognize first the re- 
semblance of the variations of species in nature to the more familiar 
variations which go on among domesticated plants and animals. 
And, secondly, he perceived that the competition for the means of 
subsistence, which the pressure of populationimposes upon the mem- 
bers of the human race, is simply one phase of 'the struggle for 
existence,' which is going on everywhere throughout the organic 
world. 

§ 66. The Incompleteness of Analogical Reasoning. — 
The most striking feature of analogical arguments is found in 
the fact that they yield only probable conclusions. And the 
reason for this is not far to seek. For, as has been already 
shown, analogy is a method of reasoning from one particular 
case to another on the basis of some imagined or perceived 
similarity between the two cases. Complete logical demon- 
stration, or certainty, however, is attained only when the new 
fact or group of facts is really and essentially united by means 
of some general principle with what is already knovv^n. There 
is no genuine inference from ^particular to particular/ as 
Mill supposed. Inference, as has been well said, always 
' proceeds through a universal.' It is the universal implied 
in the common name, or vaguely present in the mind of the 
reasoner, which really carries the inference in cases where 
conclusions appear to be drawn from a particular case. 
When one reasons that food or drink which has made A 
ill will produce the same result in B, it is the universal nature 
of human beings on which the inference is based. In the 



§ 66. Incompleteness of Analogical Reasoning 275 

case of Analogy, the inference lacks certainty because 
the universal nature is not analyzed or defined. Instead, 
it is vaguely assumed in the form of external likeness or 
resemblance. 

But, although Analogy yields only probable conclusions, 
it must not be forgotten that ' probability ' is not a fixed 
quantity. An argument from analogy may have any degree 
of value, from zero almost up to the limit of complete logical 
certainty. To fully explain or demonstrate any fact, we are 
obliged, I think, to go beyond analogy, and to verify its con- 
clusions by a method which has still to be described. It is 
evident, nevertheless, that the value of an analogical argu- 
ment will depend upon the nature of the resemblance which 
is taken as the basis of inference. In general, it is true that 
the greater the resemblance between the two cases, the more 
certainly can we reason from one to the other. This is not to 
say, however, that the value of the conclusion is in direct 
proportion to the number of points of resemblance which can 
be discovered. For example, we might reason: These two 
men are of the same height, of the same age, live in the same 
house, come from the same town; the one man stands well 
in his classes, therefore the other probably does so also. 
If the number of points of resemblance were the essential 
thing, the argument ought to possess some weight, but it is 
clear that it has none. The difficulty is that none of the 
resemblances mentioned are fundamental, or in any way 
essential to the real nature of the things compared. If we 
knew that the tv/o men were similar in character, this one 
characteristic would be worth more, as a basis for the con- 
clusion, than all the circumstances which we have mentioned 
combined. 



2/6 Analogy 

It is true, then, as Mr. Bosanquet remarks, that in analogi- 
cal reasoning we must weigh the points of resemblance rather 
than count them/ Other things being equal, the more points 
of resemblance we can make out the better; but if these are 
to contribute at all to the certainty of the conclusion, they 
must represent some deep-lying cha.racteristic of the things 
compared. In general, it must be said that it is only expe- 
rience which can inform us what resemblances are fundamen- 
tal, and what merely external. Systematic knowledge in any 
field enables us to separate the essential from the accidental. 
And, what is perhaps a corollary from this, it must not be 
forgotten that the value of an inference from analogy depends 
largely upon the amount of intellectual insight possessed by 
the mind which makes it. The ordinary mind, at least in its 
undisciplined and untutored condition, regards all things as of 
equal importance. It is therefore led away by the strongest 
stimulus — by striking external and accidental resemblances 
— as is well shown by the readiness with which such minds 
are carried away by the fallacies of figurative or analogical 
language. On the other hand, a scientific genius whose mind 
is well stored with facts, and who is gifted in addition with 
imagination, is able to penetrate beneath the surface and to 
apprehend the real or fundamental resemblance. His imagi- 
nation enables him to see beyond the chaos of the particular 
facts, and to detect the underlying principle by means of 
which these facts can be connected and systematized. 

Analogy thus becomes deepened until it passes from the 
stage of a mere argument from particular to particular, to 
the perception of a general law which includes the individual 
instance. But no such direct insight can claim the title of 

^ Logic, Vol. II., p. 99. 



§ 66. Incompleteness of Analogical Reasoning 277 

knowledge, until it is tried and tested by the facts. The 
guesses of scientific men unfortunately often prove mistaken. 
It is always necessary that fancy shall be confronted with 
facts. Even Darwin's magnificent analogical inference w^as 
nothing more than an hypothesis, as he himself well under- 
stood, until its power of explaining the facts of organic life 
was demonstrated. We have now to explain in the next 
chapter the methods by which such guesses are tested. 

REFERENCES 

J. S. Mill, Logic, Bk. III., Ch. XX 

A. Bain, Logic, Part Second, Induction, pp. 140-148. 
J. G. Hibben, Inductive Logic, Ch. XIV. 

B. Bosanquet, Logic, Vol. II., Ch. III. 

*' '^ The Essentials of Logic, pp. 155-58. 

W. Minto, Logic Inductive and Deductive, pp. 367-373. 



CHAPTER XIX 

THE USE OF HYPOTHESES 

§ 67. Reasoning from an Hypothesis. — An hypothesis, 
taken in its most general sense, is a guess or supposition as 
to the existence of some fact or law which will serve to explain 
a fact or connection of facts already known to exist. It is 
thus an expression of the tendency of the mind to leave noth- 
ing standing in isolation, but to ^ explain ' the various parts of 
experience by bringing them into relation with one another. 
^Theory ' is another word that is often used as equivalent to 
hypothesis. Strictly speaking, however, it is better usage to 
employ the term ' hypothesis ' for the unverified, or only par- 
tially verified guess, and to reserve ^ theory ' for the hypothesis 
that has been more completely demonstrated. This distinc- 
tion, however, is not usually maintained, and even in scientific 
writings the terms ^ theory ' and ' hypothesis ' are used in- 
terchangeably. Nevertheless, it is necessary to distinguish 
in some way the ^ mere hypothesis,' or supposition, which is 
often as likely to be false as true, from the hypothesis which 
has been established by proof. 

It is important to remember that it is not only in solving 
scientific problems that we employ hypotheses. In our ordi- 
nary experience, we are constantly trying to imagine the 
most likely explanation of facts which we perceive through 
the senses. If, for example, one should find on returning 
to one's room that a pane of glass had been broken, one 
would straightway set about finding some explanation of this 

occurrence. One might perhaps first imagine that a stone or 

278 



§ 6/. Reasonmg from an Hypothesis 279 

something of the kind had been thrown against it. Acting 
on this supposition, one would look for the stone in the room. 
If it were found there, the hypothesis would be confirmed; if 
no traces of it could be discovered, and if, moreover, on exami- 
nation the glass proved to be shattered in a way that would 
probably not result from the projection of a stone against it, 
our first hypothesis would have to be abandoned. We should 
then make another guess — perhaps that the outside blind 
had been violently closed by the wind — and again examine 
the facts to see if they gave any support to this supposition. 
We are constantly making hypotheses of this character to 
explain phenomena which we meet with in everyday expe- 
rience. If we find a stream swollen, we conclude that it must 
have rained in some part of the country drained by the stream. 
If a man has typhoid fever, we are pretty sure to guess that 
he has been drinking impure water. We no sooner perceive 
something unusual or striking than we begin to guess out, as 
it were, its explanation. The formation of hypotheses, then, 
is simply the mind's response to the demand for explanation. 
The examples given above illustrate what may be called 
the popular, as opposed to the scientific use of hypotheses. 
In these cases the hypothesis assumes the existence of a par- 
ticular thing or event as that through which the phenome- 
non in question is to be explained. The ^ law ' at which the 
induction arrives is that of a causal connection of phenomena 
taken in a descriptive or factual way. Analysis is not car- 
ried on to reach a genuinely explanatory hypothesis, as it 
would be in a strictly scientific investigation. Such an 
explanatory hypothesis would not point to any particular 
phenomenon as a ' cause,' but would state as a law certain 
permanent forms of relation in which things and events 



28o The Use of Hypotheses 

stand, and under which the phenomenon in question is 
assumed to fall. Think of the difference in character between 
the hypothesis that the window was broken by the slamming of 
the blind, and, for example, Newton's law of Gravitation, 
or the vast generalization of facts included in Darwin's law 
of Natural Selection. 

Nevertheless, it cannot be maintained that the distinction 
is in any sense absolute between the hypothesis of a fact 
and the hypothesis of a general law of relation. What is 
an hypothesis at one stage becomes, when verified, for fur- 
ther investigation a fact or starting point. Between the 
popular and the scientific use of hypotheses there are im- 
portant differences of degree, as has been pointed out. In 
discussing the use of hypotheses in this chapter, we shall have 
in mind primarily the reflective and critical procedure through 
which certain conceptions are defined and tested as instru- 
ments for the colligation of facts. We shall thus be study- 
ing, in its highest and most explicit form, the function that 
guides Induction from its earliest beginnings. 

It is worth noticing that it is only unusual or striking 
events, or those in which they have some practical concern, 
which attract the attention of the majority of mankind, and 
lead them to form explanatory hypotheses. What is famil- 
iar, or of no practical importance, does not usually awaken 
curiosity. Indeed, in a great many cases, such phenomena 
are not observed at all. But the great scientist is distin- 
guished, one may say, by his intellectual curiosity. He tries 
to understand phenomena which the ordinary mind neglects 
and simply takes for granted. He has questions in his mind 
with regard to familiar things which he wishes to have an- 
swered, guesses which he is desirous of having proved or dis- 



§ 6/. Reasoning from an Hypothesis 281 

proved. Unless the mind has some question to answer, or 
theory to test, it is impossible to see any significance in an 
experiment. In other words, every experiment must have 
a purpose, and the purpose is to get some information that 
will help us to answer a question which we bring with us to 
the investigation. 

In the actual process of acquiring knowledge, then, obser- 
vation and theorizing go hand in hand. Unless we go to 
nature with something in our mind, we are not likely to learn 
much. As a rule, we see only what we look for. Francis 
Darwin says of his father: ^' He often said that no one could 
be a good observer unless he were an active theorizer. This 
brings me back to what I said about his instinct for arresting 
exceptions : It were as though he were charged with theoriz- 
ing power ready to flow into any channel on the slightest 
disturbance, so that no fact, however small, could avoid 
releasing a stream of theory, and thus the fact became magni- 
fied into importance. In this way it naturally happened 
that many untenable theories occurred to him, but fortu- 
nately his richness of imagination was equalled by his power 
of judging and condemning the thoughts which occurred 
to him. He was just to his theories and did not condemn 
them unheard; and so it happened that he was willing to 
test what would seem to most people not at all worth testing. 
These rather wild trials he called ^ fool's experiments,' and 
enjoyed exceedingly. As an example, I may mention, that 
finding the cotyledons of Biophytum to be highly sensitive 
to vibrations of the table, he fancied that they might perceive 
the vibrations of sound, and therefore made me play my 
bassoon close to a plant." ^ 

^ Life and Letters of Charles Darwin^ Vol. I., p. 126. 



282 The Use of Hypotheses 

A good example of how essential theories are for an 
observer, and how blind he may be to what he is not looking 
for, is found in the work from which we have just quoted. 
In the brief autobiography contained in the first volume, 
Darwin tells of a geological trip through Wales which he took 
while a student at Cambridge, in company with Sedgwick, 
the professor of geology. It must be remembered that this 
was before Agassiz had come forward with his theory of a 
glacial period in the world's history. Darwin writes: ^^ We 
spent many hours in Cwm Idwal, examining all the rocks 
with supreme care, as Sedgwick was anxious to find fossils in 
them; but neither of us saw a trace of the wonderful glacial 
phenomena all around us; we did not notice the plainly 
scored rocks, the perched boulders, the lateral and terminal 
moraines. Yet these phenomena are so conspicuous that, 
as I declared in a paper published many years afterward in 
the Philosophical Magazine^ a house burnt down by fire did 
not tell its story more plainly than did this valley. If it 
had been filled by a glacier, the phenomena would have been 
less distinct than they are now." ^ 

§ 68. Formation of Hypotheses. — We are now ready to 
consider a little more closely the formation of hypotheses or 
theories. In the first place, it is to be noticed that hypoth- 
eses are not received from without through sense-perception, 
but are made by the mind. They are the creations of the 
imagination. A good theorizer, like a poet, is in a certain 
sense born, not made. The man to whom ^ nothing ever 
occurs,' whose intellectual processes are never lit up with a 
spark of imagination, is unlikely to make any important dis- 
coveries. It has been by a flash of scientific genius, by im- 
^ Life and Letters of Charles Darwin^ Vol. I., p. 49. 



§ 68. Formation of Hypotheses 283 

aginative insight which we may almost call inspiration, that 
great scientific theories have been discovered. Not even a 
scientific genius, however, can afford lo neglect the facts. 
But, guided by accurate observation, the scientific imagina- 
tion tries to invent some law or principle which will serve to 
connect and explain facts. Tyndall has an essay on '^ The 
Scientific Use of the Imagination,'' from which we may quote 
a short passage. ^^ With accurate experiment and observa- 
tion to work upon, imagination becomes the architect of 
physical theory. Newton's passage from a falling apple to 
a falling moon was an act of the prepared imagination. 
. . . Out of the facts of chemistry the constructive imagina- 
tion of Dalton formed the atomic theory. Davy was richly 
endowed with the imaginative faculty, while with Faraday 
its exercise was incessant, preceding, accompanying, and 
guiding all his experiments. His strength and fertility as a 
discoverer are to be referred in great part to the stimulus of 
the imagination. Scientific men fight shy of the word be- 
cause of its ultra-scientific connotations; but the fact is, that 
without the exercise of this power, our knowledge of nature 
would be a mere tabulation of coexistences and sequences." ^ 

In speaking of hypotheses as 'guesses, ' or ' creations of the imagi- 
nation, ' their dependence upon facts must not be forgotten. It is 
only when the phenomena to be explained have been carefully ob- 
served that our guesses at their explanation are likely to be of value. 
It is well known that a considerable amount of knov/ledge is usually 
required to ask an intelligent question. And in the same way, the 
mind must be well stored with facts, in order to render our hypo- 
thetical explanations worthy of consideration. Indeed, observation 
of facts and the formation of theories go hand in hand, and natu- 

^ Fragments of Science ^ p. 104. 



284 The Use of Hypotheses 

rally assist each other. We have already spoken of the lack of theory 
which makes us blind to facts that seem to lie directly before us. 
But we have perhaps not yet emphasized sufficiently the dependence 
of theories upon the facts of observation. The process of explana- 
tion may be described as a fitting together of the facts given by ob- 
servation, with the explanatory theories which the mind originates. 
The theory with which we start enables us to ask questions, and 
leads us to scrutinize the phenomena which are to be explained; 
while the latter react upon the theory, and cause it to undergo con- 
stant modification. Neither the 'theory' nor the facts are to be 
regarded as fixed and unchanging; both are constantly changing in 
relation to each other as the investigation proceeds. The account of 
Darwin's discovery of the principle of 'the survival of the fittest' is 
a good illustration of an hypothesis constructed by a constant 
dependence upon the facts during every step of its progress. 

We have already referred to the way in which analogy 
leads the mind on to general principles of explanation (§ 60) . 
Analogy is a method of inferring that what is true of one 
object is probably true of others which resemble it. But 
the ordinary mind sees resemblances only when they are 
very obvious and striking. The man of scientific insight, on 
the other hand, like the poet, penetrates more deeply into the 
nature of things, and is able to discover analogies and resem- 
blances to which the ordinary man is blind. Who but a 
genius like Newton would have thought of connecting the 
fall of an apple with the fall of the heavenly bodies through 
space ? The history of science shows that great discov- 
eries are made by means of imaginative insight, but it also 
teaches that mere imagination without dependence upon 
known facts is frequently a source of much mischief. Mere 
theories without facts are not only empty, but often stand 
in the way of true knowledge. The fruitful exercise of the 



§ 69. The Proof of an Hypothesis 285 

imagination, if we may judge from the way in which great 
discoveries have been made, always takes place in closest 
connection with what observation and experiment reveal 
regarding the nature of phenomena. If the imagination is 
to have power to discover any truth, it must constantly 
' touch earth,' and be guided in its course by the nature of 
facts which are already known. 

In framing hypotheses, then, the imagination is constantly 
prompted by analogies with processes which are more or 
less familiar. The hypothesis, accordingly, is not created by 
the imagination ' out of nothing.' It is rather an extension 
or development of a known law, than an absolute creation. 

§ 69. The Proof of an Hypothesis. — We have discussed 
the way in which hypotheses are formed, but as yet have said 
nothing regarding the means of determining their truth or 
falsity. But to form hypotheses is usually easy, to verify 
them is often exceedingly difficult. The scientific worker 
constantly finds that theories which he has formed cannot be 
verified, and must therefore be discarded. It is not only 
essential that a scientific investigator shall possess a mind 
fertile in ideas; he must also love truth more than any 
theory, no matter how interesting or attractive it may appear. 
In behalf of truth, every theory must be subjected to the 
most thorough and searching tests possible; if it is not borne 
out by facts, it must be at once discarded. What now is 
the general method of procedure in testing an hypothesis ? 
How do we proceed to compare our theories with the facts ? 
Two steps or stages may be distinguished in this process: 
(i) We assume that the hypothesis is true, and proceed to 
show what are the necessary results which follow from it. 
In doing this we proceed deductively; that is, assuming the 



286 The Use of Hypotheses 

truth of the hypothesis, we reason out what consequences 
must follow from it in accordance with laws whose mode of 
action we already know. (2) The conclusions thus reached 
are compared with the actual facts, as given to us directly 
in perception, or as determined by experiment. If they are 
found to agree with these, the hypothesis is regarded as true; 
if they do not agree, it becomes necessary to discard the 
hypothesis, or to modify it in some way suggested by the re- 
sults so far obtained by the investigation. 

This procedure may become clearer by considering some 
concrete examples. We may first take an illustration of 
what has been called the popular use of an hypothesis. If 
we were to come on the campus some morning and find that 
several branches had been broken from one of the trees, we 
should naturally try to explain this circumstance by making 
some hypothesis. Perhaps the first thing which would occur 
to us would be that there had been a violent wind storm. 
The hypothesis having been made, the next step would be to 
look around to see if it could be verified. * If there has been 
a cyclone,' we might argue, ^ there should be other signs of 
its presence; we should find broken twigs and blown leaves 
lying about, and all the trees should present a storm-tossed 
appearance.' If observation showed that these things were 
actually present, we would consider our hypothesis so far 
confirmed. But if not, our first guess would be disproved, 
and it would be necessary to look about for another expla- 
nation. In this case, the second hypothesis, being based on 
a better analysis of the facts, would be more likely to prove 
correct than the first. But the process might have to be con- 
tinued through several steps. 

An excellent illustration of the way in which a scientific 



§ 69. The Proof of an Hypothesis 287 

hypothesis may be rendered more certain and at the same 
time more comprehensive and definite is found in the history 
of the experiments by which it was proved that the atmosphere 
has weight. Gahleo noticed that water will rise in a pump only 
about '^'^^ feet. He could not find out, however, why it was that 
the water stopped at this point. After his death, his friend 
and pupil Torricelli took up the problem, and asked himself: 
Why does the water rise at all ? It then occurred to him 
that air must weigh something, and that it might be this 
weight on the surface of the water which forced the water up 
the pump when there was no air pressing it down. Now, if 
this were so, he reasoned, the weight of the air ought to lift 
mercury, which is fourteen times heavier than water, to one- 
fourteenth of the height. So he took some mercury, and 
filling a tube about 34 inches long, turned it upside down into 
a basin of mercury which was open and therefore under the 
pressure of the atmosphere. The mercury began to settle 
in the tube, and finally rested at a height of 30 inches. Tor- 
ricelli had thus invented the barometer, an instrument which 
would measure the weight of the atmosphere. It was after- 
wards suggested by the famous French writer, Pascal, that at 
the top of a high mountain, where there is less air pressing 
downwards, the column of mercury should fall considerably 
if the atmosphere were really what caused the water and the 
mercury to rise. When this experiment was made by carry- 
ing the barometer to the top of a mountain called the Puy de 
Dome, the mercury fell nearly three inches. Still further 
confirmation of Torricelli's theory was afforded by the dis- 
coveries of Otto Guericke of Magdeburg. In 1650 Guericke 
invented the air-pump. The first use which he made of his 
new invention was to show that the atmosphere is pressing 



288 The Use of Hypotheses 

down upon us heavily and equally in all directions. He 
fitted closely together two metal hemispheres and exhausted 
the air between them by means of his pump. It was found 
that the pressure of the atmosphere was so great that it took 
a great force to separate the hemispheres.^ 

To establish a scientific theory, then, there is necessary 
not only a ready imagination, but also patience and perse- 
verance in the careful deduction of the consequences of the 
theory, and in the comparison of the results thus obtained 
with the actual facts. Scientific work also demands the 
utmost candour and openness of mind on the part of those 
who engage in it. One must be willing to abandon any 
theory as soon as it is found to disagree with the facts. And 
this is by no means an easy thing to do. When one has a 
theory which suffices for nearly all the facts, there is always 
a temptation to cling to it, and to neglect or explain away 
any troublesome or contradictory facts. There is no doubt 
that the scientific explanations which have become accepted 
and established were not the ideas which first happened to 
occur to the men with whose names they are associated. 
When Newton first attempted to work out the verification of 
the gravitation hypothesis, he used the most accurate meas- 
urements he could obtain regarding the size of the earth. 
But in calculating on this basis the pull of the earth on the 
moon, and the consequent deflection of the moon from the 
straight line, his results came out wrong. That is, the moon 
moved more slowly than it ought to move according to his theory. 
The difference was not great, but Newton could not overlook 
this lack of agreement with the observed facts. He put the 
whole matter aside ; and it was only when he heard, sixteen 

1 Cf. Buckley, Short History of Natural Science, pp. 114-121. 



§ 69. The Proof of an Hypothesis 289 

years later, that Picart had discovered from new and more 
accurate measurements that the earth was larger than had 
been supposed, that he repeated his calculations, and found 
his hypothesis verified. 

(i) In stating the general theory of Induction in the opening 
Chapter (§ 50), emphasis was laid on the part played by hypotheses 
or guiding conceptions from the very beginning of an investigation. 
Frequent references to this point were also made in the discussion 
of the various methods. We learned that even to define a problem 
or ask an intelligent question is to presume something, or to have 
some kind of an hypothesis regarding the kind of answer to be 
given. The question how hypotheses are tested, is then really iden- 
tical with the question how inductions in general are established. 
Now, in explaining and illustrating the procedure of Induction 
and its use of the various methods, attention was more than once 
directed to the part played by Elimination. The inductive method 
of proof, it was said, might be represented by a Disjunctive Syl- 
logism where all the possibilities but one were eliminated by ex- 
hibiting their incompatibility with the facts. But in these earlier 
references it was also indicated that certain qualifications of this 
view are necessary. It must be borne in mind that Elimination is 
simply a means to an end, and that it therefore only partially de- 
scribes the inductive process. The fact must be emphasized that 
the real purpose of Induction, as of all thought, is to discover posi- 
tive connections and laws, and to define these as accurately as 
possible. 

When we observe facts and perform experiments in order to test 
the first hypothesis suggested by a problem, we obtain evidence 
which not merely serves to eliminate that hypothesis, but which also 
points more or less definitely in a positive direction. It is not 
generally true, then, that we approach a problem with several defi- 
nite hypotheses in mind, and proceed to try them one after another 



290 The Use of Hypotheses 

as we might try various keys at random in a lock. But, in think- 
ing, as in all genuine experimentation, failures are instructive. 
The new hypothesis is forged in and by the process of investiga- 
tion itself, just as in the progress of the arts finer and more accurate 
instruments are constantly made possible through the use of those 
already in existence. The Ptolemaic theory of astronomy, for exam- 
ple, made possible the observations and measurements which finally 
overthrew it and gave rise to the conception of Copernicus. The 
new hypothesis, then, may generally be better represented as a 
modification or closer definition of its predecessor than as some- 
thing quite new and independent. The formal representation of 
the Induction by means of the Disjunctive Syllogism, accordingly, 
fails to bring out clearly the fact of the development of knowledge 
as the work of investigation proceeds. And, as a consequence, the 
disjunctive member not eliminated is represented as if it were simply 
of coordinate importance with the others, and as if the fact that it 
was not eliminated were a mere accident. Or, put in other words, 
it fails to make clear the fact that (apart from the unmeaning 'in- 
finite judgment,' e.g. 'no good resolution is an octagon') all negation 
or elimination has positive significance, and that the inductive 
analysis, as it proceeds, furnishes positive grounds of support for 
one hypothesis in and through the exclusion of the others. An 
hypothesis must always be proved by showing its positive con- 
formity with facts : negative results and considerations taken alone 
never furnish complete inductive proof. 

In dealing with certain problems, however, or at certain stages of 
inquiry, we are often compelled to depend in large part on negative 
evidence. The fact that other hypotheses are excluded, or are less 
satisfactory, is very often given as a reason in support of a par- 
ticular theory. But in such cases there always exist, in addition, 
positive reasons in support of the theory, though they are not 
regarded as sufficiently strong to prove it completely. Moreover, 
at a particular point in an investigation, we are sometimes able 



§ 69. Tlie Proof of an Hypothesis 291 

definitely to limit the number of possibilities. We do this in mathe- 
matics, for example, when we say that one number or dimension 
is equal to, greater than, or less than, another. And the same is 
sometimes possible in other fields where we know definitely the 
exact relations of things. If we are able to say that the phenome- 
non we are trying to determine is either a, 6, or c,we can, of course, 
prove that it must be h by eliminating a and c. Outside of mathe- 
matics, however, the proof would scarcely ever depend wholly on 
the principle of Exhaustion; but in eliminating the other possi- 
bilities some positive grounds for the existence of h would almost 
certainly appear. 

(2) The method of proving an hypothesis has been described 
(page 285 f .) in the following way : ' If the hypothesis agrees with the 
facts it is to be regarded as established; if it is not in conformity 
with them, it is to be discarded as false. Now, when stated thus 
baldly, the professed method of proof seems to involve the fallacy 
of affirming the consequent (cf. p. 146). ^ If a man swallows 
prussic acid he will die; he is dead, and therefore must have 
swallowed the acid. ' This is obviously fallacious reasoning. We 
cannot infer that, because certain facts are known to exist which 
would exist if a certain hypothesis were true, the hypothesis is 
therefore true. When we speak of an hypothesis as proved by its 
ability to explain all the facts, it is evident that some further 
qualifications are necessary. From a practical point of view, an 
hypothesis is certain somewhat in proportion to the number and 
the variety of the facts that it is able to explain, assuming, of course, 
that there are no important relevant facts which it fails to explain. 
In speaking of Natural Selection, Darwin says: ^'This hypothesis 
may be tested ... by trying whether it explains several large 
and independent classes of facts ; such as the geological succession 
of organic beings, their distribution in past and present times, 
and their mutual affinities and homologies. If the principle of 
natural selection does explain these and other large bodies of facts 



292 The Use of Hypotheses 

it ought to be received." This quotation brings out the fact that 
the certainty of an hypothesis is not inferred from a single fact or 
group of facts, and is even not derived from its agreement with a 
mere sum of facts. It is rather guaranteed by what has been 
well called the * Consilience of Results.' An hypothesis is 
accepted as estabhshed when a number of large and independent 
bodies of fact all point toward it as the one conception exactly 
fitted to bring them all into intelligible relations. 

From the standpoint of logic, it is essential to prove, not only 
that the hypothesis will explain the facts, but that it is the only hy- 
pothesis which will explain them. To get this result, the other possi- 
bilities must obviously be eliminated by a more complete and exact 
survey of facts, and all the positive circumstances brought to light 
which tend to confirm the hypothesis in question. This is the func- 
tion of the ' large and independent bodies of fact ' which Darwin men- 
tions in the passage just quoted. What is achieved in this way is the 
exact fitting together of facts and hypothesis through a process of 
progressive adjustments. In the process the hypothesis is frequently 
used as a basis for the prediction of new facts, which, when they are 
found, serve in their turn to confirm the truth of the hypothesis. 
A most interesting illustration of this procedure is afforded by Dar- 
win's prediction of the existence of a species of Madagascar 
moth with a tongue eleven inches in length. The basis of the pre- 
diction was his theory of the fertilization of flowers by insects, and 
the adaptation that is consequently found between the structure 
of its parts and certain species of insects. Shortly after the ap- 
pearance of his book On Fertilization of Orchids by Insects, a cor- 
respondent wrote to him objecting to the theory elaborated in that 
work: ''What have you to say iti regard to an orchid which 
flourishes here in Madagascar possessing a long nectary, as 
slender as a knitting-needle, and eleven inches in length? On 
your hypothesis there must be a moth with a tongue eleven inches 
long, or this nectary would never have been elaborated." Darwin 



§ 70. Requirements of a Good Hypothesis 293 

replied:^ ^^The existence of an orchid with a slender nectary 
eleven inches in lengthy and with nectar secreted at its tip, is a 
conclusive demonstration of the existence of a moth with a tongue 
eleven inches in length, even though no such moth is known." 
Not long afterwards Darwin's prediction was verified by the dis- 
covery of a huge sphinx-moth with a tongue of the length pre- 
dicted. 

§ 70. Requirements of a Good Hypothesis. — Various 
conditions or requisites of a good hypothesis are laid down 
by writers on logic. The three laws which are most fre- 
quently stated are as follows: (i) That the hypothesis shall 
be conceivable and not absurd. (2) That it shall be of such 
a character that deductions can be made from it. (3) That 
it shall not contradict any of the known laws of nature. 

It does not seem to me that the first law is of much value. 
It is largely individual taste or education which leads us to 
pronounce certain theories ^absurd' or ^inconceivable.' 
Thus, for a long time, it seemed inconceivable that the earth 
should be round, and should revolve on its own axis ; and 
less than a generation ago the theory of evolution, as pro- 
pounded by Darwin, seemed to many persons utterly ^ absurd.' 
Nor can the third law always be applied as a test of an hypoth- 
esis, for many great discoveries seemed, at the time when 

^ I have taken this story from W. H. Gibson's Blossom Hosts and Insect 
Guests (pp. 28-29), but have been unable to verify it from Darwin's published 
letters. In the second edition of the Fertilization of Orchids (Ch. VI.), how- 
ever, Darwin refers to this orchid {Angr cecum sesquipedale), and from the 
length of its nectary predicts the existence of a moth with a proboscis of 
corresponding length. In the same passage he goes on to say: "This belief 
of mine has been ridiculed by some entomologists, but we now know from 
Franz Miiller that there is a sphinx-moth in South Brazil which has a pro- 
boscis of nearly sufficient length, for when dried, it was between ten and 
eleven inches long. When not protruded, it is coiled up into a spiral of at 
least twenty windings" (p. 163). 



294 The Use of Hypotheses 

they were announced, to contradict known laws of nature. 
The difficulty is that no one is able to affirm, unconditionally, 
that a law of nature forbids us to make this or that hypoth- 
esis. Of course, we feel that a theory is very probably false 
which is at variance with the law of gravity, or with that of 
the conservation of energy, or any of the laws which we 
regard as established beyond a reasonable doubt. But, 
although the chances are always very greatly against any 
theory which runs counter to what are regarded as well- 
established laws, there is yet always a possibility that it may 
be true. There is no law of nature so certain as to be in- 
fallible. Even those laws which appear to be beyond the 
possibility of doubt, may require to be modified or supple- 
mented. We may find that, practically, it is not wise to 
trouble ourselves with theories which undertake to overthrow 
the law of gravitation, or to disprove other fundamental 
laws of the physical world. But theoretically, at least, 
there is always a chance — in cases such as we have been 
supposing the chance is almost infinitely small — that the new 
theory may be right, and the old one wrong. The practical 
objection to admitting the claims of this canon is the diffi- 
culty in applying it fairly. The phrase, ^ contrary to the 
laws of nature,' like ^ inconceivable,' and ' absurd,' is likely 
to be used to condemn any theory with which one disagrees. 
In this way, it is evident that the very point is begged which 
is really at issue. 

Of these three canons, therefore, the second appears to 
state the only condition which is essential to an hypothesis. 
An hypothesis, if it is to be of any value, must be capable of 
being proved or refuted. But, unless its consequences can 
be shown by way of deduction, it is impossible to know 



§ 70. Requirements of a Good Hypothesis 295 

whether it agrees, or does not agree, with the facts which it 
is supposed to explain. An hypothesis from which nothing 
can be deduced, then, is of no value whatever. It always 
remains at the stage of mere possibility, and without any real 
connection with fact. It is a mere guess which has no sig- 
nificance whatever, for it is entirely incapable either of proof 
or of disproof. The ability of an hypothesis to lead to the 
prediction of facts not previously known to exist has some- 
times been emphasized as a test of its value. But this cir- 
cumstance, although making the hypothesis more impressive 
is not in itself a proof of its validity. Indeed, true predic- 
tions have frequently been made on the basis of hypotheses 
which were afterwards found incorrect. The essential re- 
quirement, however, is that something shall be deducible from 
the hypothesis, that it shall lead somewhere, and thus afford 
a programme for further investigation. 

(i) In general, it is possible to deduce the consequences of a 
theory only when the principle employed is analogous, in mode of 
operation, to something with which we are familiar. Thus, for ex- 
ample, it is because the ether is conceived as resembling other mate- 
rial bodies in important respects that it can be used as a principle of 
explanation. It is assumed to be elastic and capable of receiving 
and transmitting vibrations, and as spread out like other material 
bodies in space. In virtue of these similarities to other material 
substances, it is possible to deduce the consequences which such 
a substance as ether would imply, and to compare them with the 
actual facts. But if one should make the assumption that certain 
phenomena are due to some agency totally unlike anything of which 
we have any experience, a disembodied spirit, or ghost, for example, 
it would be impossible either to prove or to disprove the assertion. 
For, knowing nothing whatever of the way in which disembodied 



296 The Use of Hypotheses 

spirits act, one could not say whether the phenomena to be ex- 
plained, table-rapping, planchette-writing, etc., were or were not 
consistent with a spirit's nature and habits. 

Another example of a barren hypothesis from which no conclu- 
sions can be drawn, is afforded by the ^catastrophe ' or ^ convulsion ' 
theory in geology, which was first combated by Lyell, in his Prin- 
ciples of Geology^ published in 1830. ^^ People had so long held the 
belief that our earth had only existed a few thousand years, that 
when geologists began to find a great number of strange plants and 
animals buried in the earth's crust, immense thicknesses of rock 
laid down by water, and whole mountain masses which must have 
been poured out by volcanoes, they could not believe that this had 
been done gradually, and only in parts of the world at a time, as the 
Nile and the Ganges are now carrying down earth to the sea, and 
Vesuvius, Etna, and Hecla are pouring out lava a few feet thick 
every year. They still imagined that in past ages there must have 
been mighty convulsions from time to time, vast floods swallowing 
up plants and animals several times since the world was made, vio- 
lent earthquakes and outbursts from volcanoes shaking the whole 
of Europe, forcing up mountains, and breaking open valleys. It 
seemed to them that in those times when the face of the earth was 
carved out into mountains and valleys, tablelands and deserts, and 
when the rocks were broken, tilted up, and bent, things must have 
been very different from what they are now. And so they made 
imaginary pictures of how nature had worked, instead of reasoning 
from what they could see happening around them." ^ 

The convulsions, or catastrophes, which were thus assumed to 
take place were regarded as the result of strange incalculable forces 
whose mode of operation could never be exactly determined. 
Instead of these mysterious agencies, Lyell assumed that causes 
similar to those with which we are now acquainted had been 
acting uniformly for long ages. The nature of the causes at work 

^ Buckley, Short History of Natural Science^ pp. 441--442. 



§ 70. Requhements of a Good Hypothesis 297 

being known, it became possible to calculate the nature of the effects, 
and thus to reduce the facts of geology to order and system. As 
we have already shown, hypotheses which are to prove really ser- 
viceable are formed by extending some known principle through 
analogy to a new class of facts. The assumption of mysterious 
agencies and principles whose mode of operation is unlike any- 
thing which is known to us, does not aid in the extension of 
knowledge. 

REFERENCES 

Mill, Logic, Bk. III., Chs. XI.-XIV. 

W. S. Jevons, The Principles of Science, Ch. XXIII. 

C. Sigwart, Logic, § %2)- 

B. Bosanquet, Logic, Vol. II., pp. 155-167. 

L. T. Hobhouse, The Theory of Knowledge, Chs. XVII.-XIX. 

H. W. B Joseph, Logic, Ch. XXIII. 



CHAPTER XX 

FALLACIES OF INDUCTION 

§ 71. The Source of Fallacy. — It is necessary at the 
close of our discussion of the inductive methods, to say 
something regarding the errors to which we are most subject 
in this kind of thinking. We have seen that knowledge is the 
result of the mind's own activity, and that it grows in complete- 
ness through a persistent effort to keep distinct things which 
are different, and to connect phenomena which belong to- 
gether. Truth, in other words, is gained by intellectual activ- 
ity. And, on the other hand, we fall into error, and are led 
away by false arguments as a result of mental indolence. 
Thinking is hard work, and there is always a tendency to 
avoid it. As a matter of fact, we all think much less fre- 
quently than we suppose. Usually, we are content to follow 
familiar associations, and to repeat current phrases, without 
doing any real intellectual work. The difficulty is that we 
can get along comfortably without thinking for the most part 
— more comfortably, perhaps, than when we do think. 
Then, again, the mind is less directly under control of the will 
than the body. One may force himself to sit down at his 
desk and open a book; but it is more difficult to compel one- 
self to think. 

The only way in which we can be saved from becoming 
'intellectual dead-beats,' is by the formation of good mental 

298 



§ 72. Fallacies due to the Careless Use of Language 299 

habits. It requires eternal vigilance and unceasing strenuous- 
ness to prevent our degeneration into mere associative 
machines. What the logical doctrine of fallacies can do is to 
put us on our guard against this tendency. It enumerates 
and calls attention to some of the commonest and most danger- 
ous results of slovenly thinking, in the hope that the student 
may learn to avoid these errors. Some of the fallacies of 
Yv^hich we shall treat in this chapter, apply equally to deductive 
or syllogistic reasoning, and have been already treated in 
Chapter XI. We shall, however, enumerate them here again 
for the sake of completeness. It is convenient to discuss 
the various fallacies under the following heads: — 
(i) Fallacies due to the careless use of Language. 

(2) Errors of Observation. 

(3) Mistakes in Reasoning. 

(4) Fallacies due to Individual Prepossessions. 

After what has been said in the preceding chapters regarding 
the relation of ^ facts ' and ' theories,' it will not be supposed that 
the distinction between ^errors of Observation' and ^mistakes 
in Reasoning ' is fixed and absolute. Errors in observation re- 
sult frequently, as we have seen, from inadequate or confused 
conceptions. There is, however, a relative difference between 
the two functions of knowledge, which serves as a convenient 
principle of classification, 

§ 72. Fallacies due to the Careless Use of Language. — 
The careless and unreflective use of words is a very frequent 
source of error. Words are the signs or symbols of ideas; 
but the natural sluggishness of the mind leads often to a sub- 
stitution of the word for the idea. It is much easier to deal 
with counters than with realities. Since we must use words 
to express our thoughts, it is almost impossible to prevent them 



300 Fallacies of Induction 

from becoming our masters. Bacon, who gives the name of 
' Idols of the Market-Place ' (Jdolafori) to the fallacies which 
arise through the use of words, puts the matter in the following 
striking sentence: ^^Men imagine that their reason governs 
words whilst, in fact, words react upon the understanding; 
and this has rendered philosophy and the sciences sophistical 
and inactive." ^ The dangers connected with the use of words 
has also been well represented by Locke, from whom I quote 
the following passage: — 

^' Men having been accustomed from their cradles to learn words 
which are easily got and retained, before they knew or had framed 
the complex ideas to which they were annexed, or which were to 
be found in the things they were thought to stand for, they usually 
continue to do so all their lives; and, without taking the pains nec- 
essary to settle in their minds determined ideas, they use their 
words for such unsteady and confused notions as they have, con- 
tenting themselves with the same words other people use, as if their 
very sound necessarily carried with it constantly the same meaning. 
. . . This inconsistency in men's words when they come to reason 
concerning either their tenets or interest, manifestly fills their 
discourse with abundance of empty, unintelligible noise and jargon, 
especially in moral matters, where the words, for the most part, 
standing for arbitrary and numerous collections of ideas not regu- 
larly and permanently united in nature, their bare sounds are often 
only thought on, or at least very obscure and uncertain notions an- 
nexed to them. Men take the words they find in use amongst their 
neighbours ; and, that they may not seem ignorant what they stand 
for, use them confidently, without much troubling their heads about 
a certain fixed meaning ; whereby, besides the ease of it, they obtain 
this advantage: That, as in such discourses they seldom are in the 
right, so they are as seldom to be convinced that they are in the 

^ Bacon, Novum Organum, Aph. LIX. 



§ 72. Fallacies dice to the Careless Use of Language 301 

wrong ; it being all one to go about to draw those men out of their 
mistakes who have no settled notions, as to dispossess a vagrant of 
his habitation who has no settled abode." ^ 

(i) In treating of the misuse of words, we mention, in the 
first place, errors arising from the use of a word or phrase in 
more than one sense. This has already been described as 
the fallacy of Equivocation. In some cases, the equivocation 
may be mere wilful quibbling on the part of the person pro- 
pounding the argument, as in the following example of 
Jevons : — 

All criminal actions ought to be punished by law, 

Prosecutions for theft are criminal actions. 

Therefore prosecutions for theft ought to be punished by law. 

Examples of this kind do not mislead any one; but in some 
instances the change of meaning in words may not be per- 
ceived, even by the person who employs the argument. For 
example, one might reason : — 

It is right to do good to others, 

To assist A in obtaining office is to do him good, 

Therefore it is right to assist him in this way. 

Here the phrase which is used equivocally is, ^to do good,' 
as will at once be perceived. 

(2) Another frequent source of error in the use of words 
is found in what has been excellently named the Question- 
begging Epithet. As is well known, there is much in a 
name. The name may beg the question directly in the terms 
which it applies, or it may arouse misleading associations. 
Epithets, like 'class-legislation,' 'compromise measure,' ^a 

^ Essay Concerning Human Under standings Bk. III., Ch. X. 



302 Fallacies of Induction 

dangerous and immoral doctrine/ are terms freely used to 
describe the measures or views of opponents. And, as it is 
always easier to adopt a current phrase, than to examine the 
facts and draw our own conclusions, it is not surprising that 
the name settles the whole matter in the minds of so many 
people. Of course, the epithet employed may beg the ques- 
tion in favour of the subject it is used to describe, as well as 
against it. Politicians well understand the importance of 
adopting an impressive and sonorous election cry to represent 
the plank of their party. Thus, party cries like ^honest 
money,' 'prohibition and prosperity,' 'the people's cause,' 
etc., are essentially question-begging epithets. Even words 
like 'liberty,' 'justice,' and 'patriotism,' are frequently used 
in such a way as to bring them under the class of fallacies 
which we have here described. Under this heading, also, 
may be grouped 'cant' words and phrases. When we accuse 
a person of using cant, we always imply that he is more or less 
consciously insincere, that he is professing opinions and senti- 
ments which he does not really possess. Any insincere ex- 
pression which is made primarily for the sake of effect may 
be rightly termed cant. It is not even necessary that the 
speaker should be fully conscious of his insincerity. A man 
may easily deceive himself, and, as he repeats familiar words 
and phrases, imagine himself to be overflowing with patriotism, 
or with sympathy for others, or with religious feelings. 

(3) Figurative language is another frequent source of 
error. Of the various figures of speech, perhaps metaphors 
are the most misleading. The imagery aroused by metaphori- 
cal language is usually so strong as to make us forget the 
difference between the real subject under consideration and 
the matter which has been used to illustrate it. Thus, in 



§ 73- Errors of Observation 303 

discussing problems of mind, it is very common to employ 
metaphors drawn from the physical sciences. For example, 
we read in works on psychology and ethics of ^the struggle 
of ideas/ of 'the balancing and equilibration of motives/ of 
' action in the direction of the strongest motive/ etc. Another 
illustration, which has been often quoted, is Carlyle's argu- 
ment against representative government founded on the 
analogy between the ruler of a state and the captain of a ship. 
The captain, he says, could never bring the ship to port if it 
were necessary for him to call the crew together, and get a 
vote every time he wished to change the course. The real 
difference between the relation of a captain to his crew, and 
the executive officers in a state to the citizens, is lost sight of 
by the metaphor. Metaphors should be used only to illus- 
trate and suggest, and never to prove. Metaphorical reason- 
ing is simply a case of analogy, the imperfections and dangers 
of which have been already pointed out. It is, however, 
one of the errors which it is most difficult to avoid. A hidden 
metaphor lurks unsuspected in many of the words in common 
use. We may thus appreciate the force of Heine's humorous 
petition: ''May Heaven deliver us from the Evil One, and 
from metaphors." ^ It is, of course, not necessary or desir- 
able to abstain entirely from the use of metaphors. What is 
essential is to prevent them from ' reacting upon the understand- 
ing.' A person who is able to employ many metaphors drawn 
from various fields is perhaps less likely to be misled by 
them, than the unimaginative man — the man of one figure 
and one phrase — whose mind sticks in mechanical grooves. 
§ 73. Errors of Observation. — Sometimes insufficient 
observation is the result of a previously conceived theory; 

^Quoted by Minto, Logk, p. 373. 



304 Fallacies of Induction 

sometimes it may be due to inattention, to the difficulties of 
the case, or to lack of the proper instruments and aids to 
observation. We have already had occasion to refer to the 
influence of a theory on observation (cf. § 67). As a rule^ 
we see only those instances which are favourable to the 
theory or belief which we already possess. It requires a 
special effort of attention to take account of negative instances, 
and to discover the falsity involved in some long-standing 
belief. Indeed, it perhaps requires quite as much mental alert- 
ness to overthrow an old theory, as to establish a new one. 
It is obvious that the fallacy here is due, as is generally the 
case, to insufficient observation and analysis. The conclusion 
is based on an uncritical use of the method of Agreement, 
without any attempt to compare the positive cases with in- 
stances where the phenomenon is absent. This comparison is 
made by the method of Difference. This tendency of the 
mind to seize upon affirmative instances, and to neglect the 
evidence afforded by negative cases, is well set forth by Bacon 
in the following passage : — 

''The human understanding, when any proposition has been 
once laid down (either from general admission and belief, or from 
the pleasure it affords), forces everything else to add fresh support 
and confirmation; and although most cogent and abundant in- 
stances may exist to the contrary, yet either does not observe or 
despises them, or gets rid of and rejects them by some distinction, 
with violent and injurious prejudice, rather than sacrifice the au- 
thority of its first conclusions. It was well answered by him who 
was shown in a temple the votive tablets suspended by such as had 
escaped the peril of shipwreck, and was pressed as to whether he 
would then recognize the power of the gods; 'But where are the 
portraits of those who have perished in spite of their vows?' All 
superstition is much the same, whether it be that of astrology, 



§ 73- Errors of Observation 305 

dreams, omens, retributive judgment, or the like, in all of which the 
deluded observers observe events which are fulfilled, but neglect 
and pass over their failure, though it be much more common. But 
this evil insinuates itself still more craftily in philosophy and the 
sciences, in which a settled maxim vitiates and governs every other 
circumstance, though the latter be much more worthy of confidence. 
Besides, even in the absence of that eagerness and want of thought 
(which we have mentioned), it is the peculiar and perpetual error of 
the human understanding to be more moved and excited by affirma- 
tives than negatives, whereas it ought duly and regularly to be im- 
partial ; nay, in establishing any true axiom the negative instance is 
the most powerful." ^ 

The nature of this fallacy has been so well illustrated 
by the quotation which has just been given, that we may 
pass on at once to speak of other cases of insufificient observa- 
tion. Our discussion of the processes of reasoning have made 
it clear how necessary it is to observe carefully and attentively. 
The majority of the false theories which have appeared in 
science and in philosophy, as well as those of common life, 
have arisen from lack of observation. The doctrine of innate 
ideas, and the theory that combustion was a process of giving 
off phlogiston — a substance supposed to be contained in 
certain bodies — may be given as examples. With regard to 
phlogiston. Mill says: ^'The hypothesis accorded tolerably 
well with superficial appearances : the ascent of flame naturally 
suggests the escape of a substance; and the visible residuum 
of ashes, in bulk and weight, generally falls extremely short 
of the combustible material. The error was non-observation 
of an important portion of the actual residue; namely, the 
gaseous products of combustion. When these were at last 
noticed and brought into account, it appeared to be a universal 

^ Novum Organum, Bk. I., Aph. XLVI. 



3o6 Fallacies of Induction 

law that all substances gain instead of losing weight by com- 
bustion; and after the usual attempt to accommodate the old 
theory to the new fact by means of an arbitrary hypothesis 
(that phlogiston had the quality of positive levity instead of 
gravity), chemists were conducted to the true explanation, 
namely, that instead of a substance separated, there was, on 
the contrary, a substance absorbed.'' ^ This illustration also 
exemplifies the consequences both of neglecting Residues and 
of noticing and seeking to explain them. In some seaside 
communities, there is a belief that living beings, both human 
and animal, never die at flood tide. ^ They always go out 
with the ebb,' it is said. Again, there is a general belief, 
which was shared by such an eminent scientist as Herschel, 
that the full moon in rising possesses some power of dispersing 
the clouds. Careful observations made at the Greenwich ob- 
servatory have, however, shown conclusively that the moon 
has no such power as that supposed.^ 

Another circumstance to be considered in this connection is 
the inaccuracy and fallibility of ordinary memory. Every one 
must have noticed how rarely two persons agree completely 
jn the report which they give of a conversation which they 
have heard, or of events which they have experienced. This 
is due in part to diversity of interest: each person remembers 
those circumstances in which for any reason he is most strongly 
interested. But, in addition, it is largely the result of the in- 
evitable tendency of the mind to confuse what is actually 
observed, with inferences made from its observations. The 
inability to distinguish between what is really perceived, and 
what is inferred, is most strongly marked in uneducated 

1 Logic, Bk. v., Ch. IV. 

2 Cf. Jevons, Principles of Science, Ch. XVIII. 



§ 73- EiTors of Observation 307 

persons, who are not on their guard against this fallacy. 
An uneducated person is certain to relate, not what he actually 
saw or heard, but the impression which the events experienced 
made upon him. He therefore mixes up the facts perceived, 
with his own conclusions drawn from them, and with state- 
ments of his own feelings in the circumstances. A lawyer who 
has to cross-examine a witness is usually well aware of this 
tendency, and takes advantage of it to discredit the testimony. 
The experienced physician knows how worthless is the descrip- 
tion of symptoms given by the ordinary patient, or by sympa- 
thetic friends, or by an inexperienced nurse. The more 
one's sympathies and interests are aroused in such a case, the 
more difficult it is to limit oneself to an exact statement of 
actual occurrences. 

But this tendency is not confined to persons deficient in 
knowledge and ordinary culture. It usually requires special 
training to make one a good observer in any particular field. 
It is by no means so easy as it may appear to describe exactly 
what one has seen in an experiment. If we know, or think 
that we know, the explanation of the fact, there is an almost 
inevitable tendency to substitute this interpretation for the 
account of what has been actually observed. Recent psy- 
chological investigation, aided by exact experimental methods, 
has done much to disentangle the data of perception from 
inferences regarding these data. As every one knows who 
has practised psychological introspection, it is only with the 
utmost difficulty, and after long training, that one can distin- 
guish the actual psychological processes present to conscious- 
ness, from the associative and logical elements which are 
bound up with them in our ordinary experience. The follow- 
ing passage from Mill deals with this question: — 



3o8 Fallacies of Induction 

^'The universality of the confusion between perceptions and the 
inferences drawn from them, and the rarity of the power to discrimi- 
nate the one from the other, ceases to surprise us when we consider 
that in the far greater number of instances the actual perceptions of 
our senses are of no importance or interest to us except as marks 
from which we infer something beyond them. It is not the colour 
and superficial extension perceived by the eye that are important to 
us, but the object of which these visible appearances testify the 
presence ; and where the sensation itself is indifferent, as it gener- 
ally is, we have no motive to attend particularly to it, but acquire a 
habit of passing it over without distinct consciousness, and going on 
at once to the inference. So that to know what the sensation ac- 
tually was is a study in itself, to which painters, for example, have 
to train themselves by long-continued study and application. In 
things further rem^oved from the dominion of the outward senses, 
no one who has not had great experience in psychological analysis 
is competent to break this intense association; and when such ana- 
lytic habits do not exist in the requisite degree, it is hardly possible 
to mention any of the habitual judgments of mankind on sub- 
jects of a high degree of abstraction, from the being of God and 
the immortality of the soul down to the multiplication table, which 
are not, or have not been, considered as matter of direct intuition. " ^ 

(i) In pointing out the evils arising from confusing fact 
and theory, it is not forgotten that what are taken as ' facts ' 
are the results of earlier theorizings and interpretations (cf. 
§ 53). But the results of past processes of combination and 
comparison become embodied or fixed in more or less. definite 
form in the course of experience. Moreover, they are fixed 
in language — whether in the language of common life or in 
the technical terminology of the different sciences. There 
always is a kind of convention conveyed, both by the lan- 

1 Logic, Bk. v., Ch. IV., § 5. 



§ 74- Mistakes in Reasoning 309 

guage of ordinary life and by that of the sciences as to what 
may be taken as a fact in that court circle, — i,e, taken for 
granted as a datum or starting-point for further construc- 
tion. What is a fact in science may, of course, be an infer- 
ence from the standpoint of popular knowledge, or vice 
versa. 

Now, the fallacy against which warning is here given, arises 
from not understanding clearly what, in any given circum- 
stance, may properly be taken as ^ fact.' If there is confusion 
as to the starting-point, there is no proper basis on which 
to construct a theory. Moreover, without some certain 
starting-point, some well-ascertained datum, there is no 
means of testing and criticising our theories. 

§ 74. Mistakes in Reasoning. — The problem of the induc- 
tive processes of reasoning is to ascertain what facts are neces- 
sarily and essentially connected, and to explain this connection. 
Now, in order to distinguish between chance conjunctions of 
phenomena, and real causal connections, careful and extensive 
observation, aided whenever possible by experiment, must be 
employed. In short, to establish a real law of connection 
between phenomena, it is necessary to use one or more of the 
inductive methods described in Chapters XVI. and XVII. 
But to do this implies, in many cases, long processes of analy- 
sis; the performance of intellectual work, which ordinary 
minds, at least, have the tendency to shirk whenever possible. 
It is much easier to allow associations to control our thoughts, 
and to assume, (i) that events which happen together in our 
experience a number of times are causally connected; or, 
(2) that things that are in some way alike are causally con- 
nected, or of the same kind. We are led to such a conclusion 
by a natural psychological tendency, without taking any 



310 Fallacies of Induction 

thought about the matter, while logical analysis and discrimi- 
nation require a distinct conscious effort. 

The general name used to describe the first class of fallacies 
which are due to this particular form of mental sluggishness 
is post hoc J ergo propter hoc. Two events occur in close con- 
junction with each other, and it is then assumed without 
further investigation that they are related to each other as 
cause and effect. Many popular superstitions are examples 
of this fallacy. Some project begun on Friday turns out dis- 
astrously, and it is inferred that some causal relation existed 
between the fate of the enterprise, and the day on which it 
was begun. Or thirteen persons sit down to dinner together, 
and some one dies before the year is out. It is to be noticed 
that such beliefs are supported by the tendency, to which we 
referred in the last section, to observe only the instances in 
which the supposed effect follows, and to neglect the negative 
cases, or cases of failure. Tortune favours fools,' we exclaim 
when we hear of any piece of good luck happening to any one 
not noted for his wisdom. But we fail to take account of the 
more usual fate of the weak-minded. The belief that the 
full moon in rising disperses the clouds, which was also 
quoted earlier, is a good example of post hoc, propter hoc. 
In fact, all the fallacies treated in this chapter, except those 
due to language, might quite properly be included under 
this heading. The tendency to neglect negative instances 
-^ was given by Bacon as the most striking example of the ^ Idols 
of the Tribe' {Idola tribus), i.e. of the species of fallacies to 
which the whole tribe or race of men are subject. 

A special case of this fallacy, to which attention may be 
called separately, arises from hasty generalization, or generali- 
zation on an insufficient basis of fact. The term ^ generaliza- 



§ 74* Mistakes in Reasoning 311 

tion' is often used in logic to denote the whole inductive move- 
ment of thought from particular facts to general principles 
and laws. But the fallacy to which reference is here made 
usually concerns a special stage in that process — the stage 
where a first generalization is made from instances. We 
are said to generalize when, after a more or less extended and 
careful set of observations, we take the instances observed as 
typical of all phenomena of the same field, or of the same 
general character. When due care has not been exercised 
in making the observations or when the observations are few 
in number, or all drawn from a limited part of the whole 
field, we speak of ^ hasty generalization.' Thus it is not un- 
usual to hear a traveler declare, on the basis of a very limited 
experience, that ^ the hotels of some city or country are 
thoroughly bad.' The generalizations which are so fre- 
quently made regarding the peculiar characteristics of Ameri- 
cans, or Englishmen, or Frenchmen are usually of the same 
sort. Conclusions regarding the effect of moral and political 
conditions, too, are often drawn from observations in a limited 
field. Even scientific books are not always free from this 
error. In a recently published psychological study of the 
first year of the life of a child, by the mother, it was explained 
why a baby alvN^ays sucks its thumb rather than its fingers. 
The explanation was that the thumb, being on the outside and 
projecting outwards, got oftenest into the baby's mouth, 
and so the habit was formed. The point is, that the mother 
assumed what she had observed in her own child to be true 
universally. Other parents, however, declare that their 
babies never put the thumb into the mouth, but always the 
fingers or the whole hand. 

Another fallacy belonging to this group arises from the 



312 Fallacies of Induction 

uncritical use of Analogy. False Analogy is closely connected 
with the fallacies of figurative language. Indeed, the latter type 
of fallacies, almost without exception, arise from a loose use of 
Analogy. It has been pointed out (§ 66), that the value of 
an inference from Analogy depends upon the 'depth' or 'im- 
portance' of the resemblances upon which it is based. False 
inferences arise in every field from taking some striking or 
surface resemblance as the basis of a conclusion. Nothing 
is easier than to be led uncritically by vague resemblances, or 
even to imagine them where they do not exist. Vague or 
fancied analogies are the foundation of many popular super- 
stitions regarding omens, illness, cures, etc., and also play 
an important part in many of the sympathetic and imita- 
tive practices of Magic. 

§ 75. Fallacies due to Individual Prepossessions. — Bacon 
named this class of fallacy ''The Idols of the Cave." Each 
individual, as he represents the matter, is shut up in his own 
cave or den; that is, he judges of things from his own individ- 
ual point of view. In the first place, one's inclinations and 
passions, likes and dislikes, pervert one's judgment. It is 
exceedingly difficult, as we all know, to be fair to a person 
we dislike, or to refrain from judging too leniently the short- 
comings of those to whom we are warmly attached. Again, 
it is not easy to put oneself in the position of an impartial 
spectator when one's interests are at stake. "The under- 
standing of men," says Bacon, " resembles not a dry light, but 
admits some tincture of the passions and will." Furthermore, 
each individual has a certain personal bias as a result of his 
natural disposition and previous training. Thus it is almost 
impossible for an individual to free himself from national 
prejudices, or from the standpoint of the political party, or the 



§ 75' Fallacies dice to Individual Prepossessions 313 

church in which he was brought up. Or, if a person does 
give up his old views, he not infrequently is carried to the 
opposite extreme, and can see no good in what he formerly 
believed. Even education and the pursuit of special lines of 
investigation may beget prejudices in favour of particular sub- 
jects. When a man has been engaged exclusively for a long 
time in a particular field, employing a particular set of con- 
ceptions, it is almost inevitable that he should look at every- 
thing with which he has to do in the same light. The mathe- 
matician's view of the world is almost sure to be different 
from that of the historian, or that of the student of aesthetics. 
It is very difficult for the physicist to conceive of any natural 
process except in terms of molecules and vibrations. It is 
inevitable that each man should be blinded to some extent 
by his own presuppositions. But to recognize one's limi- 
tations in this respect, is to pass, to some extent at least, 
beyond them. 

(i) Moreover, each age, as well as each individual, may be re- 
garded as governed largely by current presuppositions and preju- 
dices. Bacon does not, however, classify the errors into which 
one may be led by the spirit of the time {Zeitgeist)^ or the beliefs 
derived from the past, with the 'Idols of the Cave,' but speaks 
of them rather as ''Idols of the Theatre." (Idola theatri). He 
draws his examples of this from the influence which the traditions 
of the Schoolmen still continued to exert in his own day. 
Throughout the Middle Ages, theological doctrines and opinions 
controlled almost absolutely the opinions and beliefs of man- 
kind. This influence, doubtless, still makes itself felt, but people 
are now pretty generally awake to the dangers from this source. 
On the other hand, it is more difiicult to realize at the present 
time that it is not impossible for prejudices and prepossessions 



314 Fallacies of Induction 

to grow out of scientific work. The success of modern scientific 
methods has sometimes led investigators to despise and belittle 
the work of those who do not carry on their investigations in 
laboratories, or do not weigh and measure everything. But con- 
ceptions and methods which prove useful in one science cannot 
always be employed profitably in another. A conception, or 
mode of regarding things, which has proved serviceable in one 
field is almost certain to dominate a whole age, and to be used as 
an almost universal principle of explanation. The eighteenth 
century, for example, was greatly under the influence of mechanical 
ideas. Newton's discovery made it possible to regard the world 
as a great machine, the parts of which were all fitted together 
according to the laws of mechanics. This view led to such a 
vast extension of knowledge in the realm of physics and astron- 
omy, that the conceptions upon which it is based were applied 
in every possible field — in psychology, in ethics, in political 
science. The world itself, as well as religious creeds and political 
and social institutions, were supposed to have been deliberately 
made and fashioned by some agent. Again, at the present time 
we are dominated by the idea of evolution. The biological notion 
of an organism which grows or develops has been applied in every 
possible field. We speak, for example, of the world as an organ- 
ism rather than as a machine, of the state and of society as organic. 
And the same conception has been found useful in explaining the 
nature of human intelligence. It is easy for us to realize the 
limitations and insufficiency of the notion of mechanism as em- 
ployed by the thinkers of the eighteenth century. But it is not 
improbable that a future century may be able to see more 
clearly than we are able to do, the weaknesses and limi- 
tations of the conception which has proved so fruitful in this 
generation. 



§ 75- Fallacies due to Individual Prepossessions 315 _ 

REFERENCES 

Bacon, Novum Organum, Aph. XXXVIII. -LXVIII. 
Locke, Essay Concerning Human Understandings Bk. III., Chs. X. 
and XI. 

J. S. Mill, Logic, Bk. V. 

A. Bain, Logic , Pt. II., Induction, Bk. VI. 

J. Fowler, Inductive Logic, Ch. VI. 

J. G. Hibben, Inductive Logic, Ch. XVII. 

A. Sidgwick, Fallacies [Int. Scient. Series]. 



PART III. — THE NATURE OF 
THOUGHT 

CHAPTER XXI 

JUDGMENT AS THE ELEMENTARY PROCESS OF THOUGHT 

§ 76. Thinking the Process by which Knowledge grows 
or Develops. — Logic was defined (§ i) as the science of 
thinking, and we have seen that the business of thought 
is to furnish the mind with truth or knowledge. Under 
what general conception, now, shall we bring thinking, 
and what method shall we adopt to aid us in its investi- 
gation? It is at once clear that thinking, the conscious 
process by which knowledge is built up, does not resemble 
mechanical processes like pressure, or attraction and re- 
pulsion. It is more nearly related to something which has 
life, like a plant or an animal, and which grows or develops 
from within, in accordance with the laws of its own nature. 
Thinking must be regarded rather as a living process, than 
as a dead thing, though it is necessary also to remember 
that it is conscious as well as living. 

When the thinking process is regarded in this way, more- 
over, a method of procedure at once suggests itself. In 
these days we have become familiar with the notion of evolu- 
tion or development, and the application of this notion has 
proved of the greatest service to science, and particularly 
to those sciences which deal with the phenomena of life. 

What is characteristic of this manner of regarding things 

316 



§ "JJ, Law of Evolution and its Application to Logic 317 

is the fact that it does not consider the various phenomena 
with which it deals as fixed, unchangeable things, each 
with a ready-made nature of its own. But each thing is 
simply a stage of a process, a step on the way to something 
else. And the relations of the various phenomena to each 
other, their connection and unity as parts of the one process, 
come out more clearly when viewed in this way. In other 
words, by taking a survey of the genesis and growth of 
things, or the way in which they come to be, we gain a truer 
idea of their nature and relations than would be possible 
in any other way. The past history of any phenomenon, 
the story of how it came to be what it is, is of the greatest 
possible service in throwing light upon its real nature. Now, 
one cannot doubt that this conception will also prove ser- 
viceable in the study of logic. That is to say, it will assist 
us in gaining a clearer idea of the nature of thinking, to con- 
ceive it as a conscious function, or mode of acting, which 
unfolds or develops in accordance with the general laws of 
organic evolution. And this process may be supposed 
to go on both in the individual, as his thought develops and 
his knowledge expands, and in the race, as shown by its 
history. By adopting this notion, we may hope to show 
also that there is no fundamental difference in kind between 
the various intellectual operations. Judgment and Infer- 
ence, for example, will appear as stages in the one intellec- 
tual process, and the relation between Induction and Deduc- 
tion, as each having its own work to do, will become evident. 
§ 77. The Law of Evolution and its Application to Logic. 
— The most striking characteristic of any organism at a 
low stage of development is its almost complete lack of 
structure. An amoeba, for example, can scarcely be said 



3i8 Jicdgment as the Elementary Process of Thought 

to have any structure ; it is composed of protoplasm which 
is almost homogeneous, or of the same character throughout. 
When we compare an amoeba, however, with an animal 
much higher in the scale of life, e,g, a vertebrate, a great 
difference is at once evident. Instead of the simple, homo- 
geneous protoplasm, the organism is composed of parts 
which are unlike, or heterogeneous, such as bones, muscles, 
tendons, nerves, blood-vessels, etc. In Mr. Spencer's lan- 
guage, there has been a change from a state of homogeneity, to 
one of heterogeneity. The process of evolution from the lower 
organism to the higher has brought with it a differentiation 
of structure. That is, in the amoeba there are no special 
organs of sight, or hearing, or digestion, but all of these acts 
seem to be performed by any part of the organism indiffer- 
ently. In the vertebrate, on the other hand, there is division 
of labour, and a separate organ for each of these functions. 
One may also notice that the same change is observable 
when the acts or functions performed by a lower organism 
are compared with those of a higher. The life of the amoeba 
seems to be limited almost entirely to assimilation and repro- 
duction; while, when we advance from the lower animals 
to the higher, and from the higher animals to man, there is 
an ever- increasing complexity and diversity in the char- 
acter of the actions performed. We thus see how the process 
of evolution involves differentiation both of structure and 
oi function J in passing from the homogeneous to the hetero- 
geneous. 

But differentiation, or increase in diversity, is only one 
side of the process of evolution. As we pass from a lower to 
a higher stage, the various parts of an organism are seen to 
become more essential to one another. If certain plants or 



§ J J. Law of Evolution and its Application to Logic 319 

low animal organisms are divided into several parts, each 
part will go on living. Its connection with the other parts 
does not seem to have been at all necessary to it. But when 
we are dealing with higher forms of life, each part is seen 
to have its own particular function, and to be essential to 
the other parts, and to the organism as a whole. In other 
words, the parts now become members, and the whole is 
not simply an aggregation of parts or pieces, but is consti- 
tuted by the necessary relation of the members to one 
another. The more highly evolved the whole with which 
we are dealing, the more closely connected and essential 
to one another are the various parts seen to be. It becomes 
increasingly true that if one member suffers, all the other 
members suffer along with it. The same principle is illus- 
trated by the relation of classes and individuals in modern 
society. In spite of the conflicts between capital and labour, 
between rich and poor, it is becoming increasingly evident 
that the unity of society is more fundamental than its dif- 
ferences and antagonisms. 

Evolution, then, not only exhibits a constant process of 
differentiation, and a constant increase in the diversity of 
parts and organs, but there goes along with this what might 
be called a process of unification, whereby the parts are 
brought into ever closer and more essential relation to one 
another. In this way, a real or organic whohj as opposed 
to a mere aggregate, is formed. This is what Mr. Spencer 
calls the process of integration; and it accompanies, as 
we have seen, what the same writer calls differentiation. 

The application of this general law of evolution to the 
development of the thinking process is not difficult. We 
shall expect to find that thinking, in its first beginnings, 



320 Judgment as the Elementary Process of Thought 

both in the individual and in the race, will be much less 
complex and differentiated than at a higher stage. That 
is, the earliest or simplest thinking tends to take things in 
a lump, without making any distinctions. The infant, for 
example, does not distinguish one person from another, or 
perhaps does not distinguish even the parts of its own body 
from surrounding objects. Now, it is clear that intellectual 
development, growth in knowledge, must in the first place 
involve differentiation. What is complex must be analyzed 
or separated into its various parts. Things which are differ- 
ent must be distinguished and clearly marked off from one 
another. The development of thought implies, then, as one of 
its moments, discrimination or analysis — what we previously 
called differentiation. 

The other moment of the law of evolution, integration, 
also finds a place in the development of thought, and goes 
hand in hand with the former. The child and the unedu- 
cated man not only often fail to make distinctions where 
these really exist, but the parts of their knowledge are frag- 
mentary, and have little or no relation to one another. The 
various pieces of their knowledge are like the parts of the 
amoeba — they may be increased or diminished without 
themselves undergoing any change. But, in order to pass 
from a lower to a higher intellectual point of view, — to 
become better educated, in a word, — it is necessary to see 
the way in which the various pieces of our knowledge are 
connected and dependent upon one another. It is not enough 
to analyze and keep separate things which are distinct, but 
it is also necessary to understand how the various parts of 
our knowledge are inter-related and essentially dependent on 
one another. In other words, we may say that it is character- 



§ "J J, Law of Evolution and its Application to Logic 321 

istic of our intelligence to endeavour to put things together so 
as to form a whole, or system of interconnected parts. And 
the more completely it is able to do this (provided that the 
process of differentiation has also made a corresponding ad- 
vance), the higher is the stage of development which has been 
attained. The ideal of knowledge, or of complete intellectual 
development, would be to understand the oneness and rela- 
tion of everything which exists, even of all those things 
which seem now to be entirely different in kind. A know- 
ledge of any one fact would then carry with it a knowledge 
of every other fact. Or, rather, our knowledge would be so 
completely unified, that each part would show the nature of 
the whole or system to which it belongs; just as a leaf of a 
plant, or a tooth of an animal, may be sufficient to tell the 
naturalist of the wholes to which they belong. 

This, of course, will always remain an ideal; but it is 
in this direction that thinking actually develops. It is a 
step in advance to discover the reasons for any fact which 
one previously knew as a mere fact. For, to discover the 
reasons for a fact, is to bring it into connection with other 
facts, to see them no longer as isolated and independent, 
but as belonging together to one group or system of facts. 
And the further the process of explanation goes on, the more 
completely is our knowledge unified and related. 

There is, however, another fact implied in the very nature 
of evolution^ of which logic, as well as the other sciences, 
may take advantage. We have assumed that the more com- 
plete and difficult kinds of thinking have grown or devel- 
oped from simpler types of the same process, and not from 
something different in kind. It will therefore follow, that 
the essential characteristics of the thinking process may be 



322 Judgment as the Elementary Process of Thought 

discovered in its simplest and most elementary form. It 
is found that all the essential functions of the fully developed 
organism are discharged by the primitive cell. And be- 
cause it is easier to study what is simple than what is com- 
plex, the cell is taken as the starting-point in biology. Simi- 
larly, there will be an advantage in beginning with the sim- 
plest and most elementary forms of thinking. What is 
found true of these simple types of thought, may be assumed 
to be essential to the thinking process as such. 

§78. Judgment as the Starting-point. — What, then, 
is the simplest form of thinking ? What shall we take as 
a starting-point, which will correspond to the cell in biology, 
or the elementary process in psychology ? To answer this 
question, it is not necessary first to decide where in the scale 
of animal life .that which we are entitled to call thinking 
actually begins. We shall not be obliged to discuss the 
much-debated question, whether or not dogs think. Wher- 
ever thinking may be found, it is essentially an activity of 
the mind. When it is present, that is, there is always intel- 
lectual work done, something interpreted or put together, 
and a conclusion reached. One may perhaps say that think- 
ing is simply the way in which the mind puts two and two 
together and sees what the result is. It implies that the 
mind has waked up to the significance of things, and has 
interpreted them for itself. Suppose that one were sitting in 
one's room very much engaged with some study, or wrapped 
up in an interesting book, and suppose that at the same time 
the sound of a drum should fall upon one's ears. Now, the 
sound sensations might be present to consciousness without 
calling forth any reaction on the part of the mind. That 
is, we might be so intent on our book that we should not 



§ 78. Judgment as the Starting-point 323 

wake up, as we have been saying, to the meaning or sig- 
nificance of the drum-taps; or perhaps not even to the fact 
that they were drum-taps at all. But if the mind did react 
upon the sound sensations, it would try to interpret them, 
or put them together so as to give them a meaning. As a 
result, some conclusion would be reached, as, for example, 
^ the drum is beating ' ; or sufficient intellectual work may 
have been done to give as a conclusion, ' that is the Salva- 
tion Army marching up the street.' In any case, it is of the 
greatest importance to notice that the conclusion does not 
come into our minds from without, but that it is the product 
of the mind's own activity, as has been described. It is 
not true, in other words, that knowledge passes into our 
minds through the senses; it is only when the mind wakes 
up to the meaning of sensations, and is able to put them to- 
gether and interpret them, that it gains any knowledge. 

Now, the simplest form of such an act of thought is called 
a judgment. Judgment, we may say, is a single intellec- 
tual act of the kind we have described; and its conclusion 
is expressed by means of a Proposition; as, for example, 
' the grass is green,' ' the band is playing.' In accordance 
with general usage, however, we may use the term ^ Judg- 
ment ' for both the act itself and its result. And the word 
' Proposition ' will then denote the external expression in 
speech or writing of the product of an act of judgment. 

In our investigation of the nature of thought, then, we 
must begin with Judgment. There are three things which 
we shall have to do: (i) To endeavour to discover the funda- 
mental characteristics of this simple type of thinking; (2) To 
show the various forms which it assumes, or to describe 
the different kinds of Judgment; and (3) To trace the process 



324 Judgment as the Elementary Process of Thought 

by which Judgment expands into the more complete logical 
form of Inference. Before any of these questions are con- 
sidered, however, it is necessary to meet a very serious objec- 
tion to our whole procedure of beginning with Judgment 
as the elementary process of thinking. 

§ 79. Concepts and Judgment. — In the last section, 
we endeavoured to show that Judgment is the elementary 
process of thought, and that with it all knowledge begins. 
The same position was also maintained in an earlier chap- 
ter (§ 11). This view, however, may seem to be contra- 
dicted by the treatment of Judgment usually found in logical 
text-books. 

Judgment, it is said, is expressed by a proposition; and a 
proposition is made up of three parts, subject, predicate, 
and copula. Thus in the proposition ' iron is a metal,' 
^iron' is the subject, ^a metal' the predicate, and the two 
terms are joined or united by means of the copula 'is.' A 
Judgment is therefore defined as an act of joining together, 
or, in negative judgments, of separating, two concepts or 
ideas. If this account be accepted, it follows that the ideas 
of which the judgment is composed (iron and metal, in 
the example given above) are pieces of knowledge which 
precede the judgment itself. And the act by which these log- 
ical ideas (or, as they are usually called, concepts) are formed 
must also be earlier and more fundamental than the act of 
judging. It is therefore held that logic should begin with 
concepts, which are the elements out of which judgments 
are compounded, and that the first logical act consists in the 
conception or simple apprehension of the ideas or concepts. 

It is necessary to examine this position very carefully. 
What is maintained is that a process of forming concepts^ 



§ 79- Concepts and Judgment 325 

or logical ideas, presumably quite distinct from the activity 
of judgment, necessarily precedes the latter. Before it is 
possible to judge that ^ iron is a metal/ for instance, one 
must have gained, by means of Conception or Apprehension, 
the ideas denoted by the subject and predicate of this proposi- 
tion. Judgments, that is, are made or compounded out of 
something different from themselves. 

It may be well to begin the defence of our own position 
by noting what is undoubtedly true in what has just been 
stated. In making a judgment like ^iron is a metal,' it is, 
of course, necessary to have the concept ^ iron,' and the 
concept ^ metal.' But what is implied in having a concept 
of anything ? Let us suppose that a person is making the 
above-mentioned judgment for the first time — that is, 
really drawing a conclusion for himself, and not merely 
repeating words. He would begin, we may say, with the 
concept Mron.' But if this concept is more than a mere 
word, if it really means anything, it must have been formed 
by a number of judgments. The concept ^iron,' if it has 
any significance for the person using it, means a definite 
way of judging about some substance — that it is hard, 
malleable, tough, etc. The greater the number of judg- 
ments which the concept represents, the more meaning or 
significance it has ; apart from the judgment, it is a mere 
word, and not a thought at all. 

To admit, then, that in judging we always start from 
some concept, does not imply that there is a different form of 
intellectual activity prior to judgment, which furnishes the 
latter with ready-made material for its use. But, as we 
have seen, in ordinary judgments like the example with 
which we have been dealing, the new judgment is a further 



326 Judgment as the Elementary Process of Thought 

expansion or development of a previous set of judgments 
which are represented by the concept. The concept, then, 
stands for the series of judgments which have already been 
made. Language comes to the aid of thought, and makes it 
possible to gather up such a set of judgments and represent 
them by a single expression — often by a single word. Every 
word which is the name of some logical concept represents 
intellectual work — the activity of judgment — in its forma- 
tion. In learning our own language, we inherit the word 
without doing the work. But it must never be forgotten 
that the word in itself is not the concept. To make the 
thought our own, to gain the real concept, it is necessary to 
draw out or realize to ourselves the actual set of judgments 
for which the word is but the shorthand expression. 

The view which regards the judgment as a compound of 
two parts — subject and predicate — rests upon the substitu- 
tion of words for thoughts. It analyzes the proposition (the 
verbal or written expression of the judgment), instead of the 
judgment itself. In the proposition, the parts do exist 
independently of each other. The subject usually stands 
first, and is followed by the predicate. But there is no such 
order of parts in a judgment. When one judges, ^ it is raining,' 
or, ^that is a drum,' the piece of knowledge is one and indi- 
visible. And the act by which this knowledge is gained is 
not an external process of joining one part to another, but 
is an intellectual reaction by which we recognize that some- 
thing, not previously understood, has a certain meaning or 
significance. 

Again, it is only when concepts are identified with the words 
which make up the parts of the proposition, that they can be 
regarded as ready-made existences which are quite independ- 



§ 79- Concepts and Judgment 327 

ent of their connection in a judgment. The terms ' iron ' and 
^ metal ' are separable parts of the proposition and exist inde- 
pendently of their connection with it. The conclusion has 
been therefore drawn that concepts had a like independence 
of judgments, but might enter into the latter and form a part 
of them without affecting their own nature in any way. 
But, as we have already seen, the concept has no meaning 
apart from the series of judgments which it represents. And, 
as thinking goes on, and new judgments are made, its nature 
is constantly changing. In short, concepts are not dead 
things^ but living thoughts which are in constant process of 
development. 

The objection, then, which urges that conception is a logical 
process that is prior to judgment, turns out, when rightly 
understood, to be no objection at all. For, in the light of what 
has been already said, it only amounts to this: In making new 
judgments regarding anything, we must set out from what 
we already know of it, as represented by the judgments already 
made. That is, the starting-point for a new judgment is the 
concept or series of judgments which represents the present 
state of our knowledge. The progress of knowledge is not 
from the unknown to the known, but from a state of partial 
and incomplete knowledge to one of greater perfection. Thus 
the judgment ^ gold is malleable ' (supposing it to be a genuine 
judgment made for the first time) adds to, or develops 
farther, our existing knowledge of gold, as represented by a 
series of judgments previously made regarding it. 

It may be urged, however, that not every judgment can grow out 
of previous judgments in this way. For, if we go back far enough, 
we must reach some judgment which is absolutely first, and which 
presupposes no antecedent judgment. This is like the paradox 



328 Judgment as the Elementary Process of Thought 

regarding the origin of life. If all judgments are derived from an- 
tecedent judgments, how was it possible for the first one to arise ? 
It will, perhaps, be sufficient answer to deny the existence of the 
paradox. Consciousness must be regarded as having from the first 
the form of a judgment. No matter how far one goes back in the 
history of consciousness, one will always find, so long as conscious- 
ness is present at all, some reaction, however feeble, upon the 
content, and something like knowledge resulting. Even the con- 
sciousness of the newly born infant reacts, or vaguely judges, 
in this way. These primitive judgments are, of course, very weak 
and corifused, but they serve as starting-points in the process of in- 
tellectual development. Growth in knowledge is simply the pro- 
cess by means of which these vague and inarticulate judgments are 
developed and transformed into a completer and more coherent 
experience. 

REFERENCES 

W. S. Jevons, Elementary Lessons in Logic, pp. 9-16. 
F. H. Bradley, The Principles of Logic, Bk. I., Ch. I. 

B. Bosanquet, Logic, Vol. I., Ch. I., §§ 1-6. 

H. Lotze, Logic (Eng. trans.), Vol. I., pp. 13-61. 

C. Sigwart, Logic, §§40-42. 

L. T. Hobhouse, The Theory of Knowledge, Pt. L, Chs. I. and II. 



CHAPTER XXII 

THE MAIN CHARACTERISTICS OF JUDGMENT 

§ 80. The Universality of Judgments. — We have now 
to examine the nature of Judgment a Httle more closely than 
has been done hitherto. In the first place, we note that 
all judgments claim universality. There are, however, 
several kinds of universality, and more than one sense in 
which a judgment may be said to be universal. We speak of 
a universal judgment (more properly of a universal propo- 
sition), when the subject is a general term, or is qualified by 
some such word as ^all,' or ' the whole.' And we distinguish 
from it the particular judgment, where the subject is only the 
part of some whole, and is usually preceded by ' some,' or 
by other partitive words. But here we have no such dis- 
tinction in mind; we are speaking of the universality which 
belongs to the very nature of Judgment as such, and which 
is shared in by judgments of every kind. 

When we say that judgments are universal, in the sense 
in which the word is now used, we mean that the conclusions 
which they reach claim to be true for every one. No matter 
what the subject and the predicate may be, a judgment, e,g, 
^ man is mortal,' comes forward as a fact for all minds. We 
have shown in the last chapter that it is by judging, or putting 
things together for itself, that the human mind gains know- 
ledge. Now, the assumption upon which this process is 
based is that the result thus reached — knowledge — is not 

329 



330 The Main Characteristics of Judgment 

something merely individual and momentary in character. 
When I judge that ' two and two are four,' or that ' iron has 
magnetic properties/ the judgment is not merely a statement 
of what is going on in my individual consciousness ; but it 
claims to express something which is true for other persons 
as well as for me. It professes to deal with facts which are 
true, and in a sense independent of any individual mind. 
The judgments by which such conclusions are reached are 
universal, then, in the sense that they are asserted as true for 
every one and at all times. The word ^ objective ' has essen- 
tially the same meaning. Although each man reaches truth 
only by actually judging for himself, yet truth is objective, 
out there beyond his individual or ^ subjective ' thought, 
shared in by all rational beings. The assumption upon 
which all argument proceeds is that there is an objective stand- 
ard, and that if people can be made to think they will arrive 
at it. Thought is in essence a process of self-criticism; for 
it has in itself its own standard of truth, which comes to light 
in and through the process of development. 

(i) The only alternative to this position is scepticism, or pure 
individualism. If Judgment is not universal in the sense that it 
reaches propositions which are true for everybody, it is of course im- 
possible to find any standard of truth at all. The judgments of any 
individual in that case would simply have reference to what seemed 
true to him at the moment, but could not be taken to represent any 
fixed, or permanent, truth. Indeed, if one regards Judgment as 
dealing merely with particular processes in an individual mind, the 
ordinary meanings of truth and falsehood are completely lost, and it 
becomes necessary to give a new definition of the words. This was 
the position of the Sophists at the time of Socrates (cf. § 5). Each 
individual man was declared to be the measure of what is true and 



§ 8i. The Necessity of Judgments 331 

false, as well as of what is good and bad. There is thus no other 
standard of truth or value than the momentary judgment (or ca- 
price) of the individual. This is, in a way, the reductio ad 
absurdum of scepticism. 

The common nature of truth, as something in which all can 
share, presupposes, then, a common mode of thinking or judging on 
the part of all rational beings. And it is this universal type or form 
of knowing with which logic deals. The question as to whose 
thought is investigated, or in what individual mind the thought 
takes place, is in itself of no importance. The consciousness of a 
savage differs very greatly from that of an educated man ; it is much 
less complex and less highly developed. But yet, in spite of the 
enormous differences, there exists in both an intelligence, or way of 
thinking, which shows the same essential character, and operates 
according to the same fundamental laws. 

§ 81. The Necessity of Judgments. — The second char- 
acteristic which we note as belonging to Judgment is necessity. 
By this we mean that when a person judges, he is not free 
to reach this or that conclusion at will. As an intellectual 
being, he feels bound to judge in a certain way. This is 
sometimes expressed by saying that we cannot believe what 
we choose ; we must believe what we can. 

In many of the ordinary judgments of everyday life, which 
are made without any clear consciousness of their grounds, 
logical necessity is implicitly present as an immediate feeling 
of certainty. In cases of this kind, we simply identify our- 
selves with the judgment, and feel that it is impossible that 
it can be false. But, of course, no judgment can claim to be 
necessary in its own right. Its necessity comes from its con- 
nection with other facts which are known to be true. Or, in 
logical terms, we may say that it comes from reasons or prem- 



332 The Main Characteristics of Judgment 

ises which support it. And one should always be ready to 
show the grounds or reasons upon which one's feeling of ne- 
cessity rests. But in ordinary life, as we have said, it is not 
unusual to regard a conclusion as necessary, without clearly 
realizing the nature of the reasons by which it is supported. 
An uneducated man is rarely able to go back and discover the 
reasons for his belief in any statement of which he is con- 
vinced. If you question his assertion, he feels that you are 
reflecting upon his veracity, and consequently grows angry. 
In the feeling of immediate necessity or conviction, he iden- 
tifies himself with the judgment, and does not see that the 
criticism is not directed against the latter, but against the 
grounds by which it is supported. 

In this distinction between necessity that is merely felt^ 
and the necessity that is conscious of its own grounds, we see 
the direction in which judgment must develop. In the evolu- 
tion of thought, we gradually become conscious of the 
grounds upon which our judgments are made. That is, the 
simple judgment, which seems to stand in isolation, is seen 
to expand so as to include its reasons as an organic part of 
itself. By itself, it is only a fragment of a more complete 
and widely embracing thought. The feeling of necessity is an 
evidence of its dependence and connection, though this de- 
pendence and connection upon other facts may not be clearly 
understood. But what is implicit must be made explicit; 
the necessity which is merely felt to belong to the simple 
judgment must be justified, by showing the grounds or rea- 
sons upon which it rests. And, for this purpose, the simple 
judgment has to be brought into relation with other facts 
and judgments which are outside of it, yet constitute its 
reasons, or are necessary to support it. In other words, it 



§ 8 1. The Necessity of Judgments 333 

must develop into an inference. As a matter of fact, the 
same form of words as used by different persons, or by the 
same person at different times, may express either a judg- 
ment or an inference. Thus, ^ the price of wheat rose after 
the war began ' might express either a simple historical fact, 
which is accepted from experience or from hearsay, or it 
might, in the mouth of a person acquainted with the laws of 
supply and demand, be the necessary conclusion of a number 
of premises. Again, a child might read that, ^ the travelers 
found great difficulty in breathing when they reached the top 
of the mountain,' accepting this as a simple statement of fact. 
If he were to read this same statement some years later, how- 
ever, he would probably connect it at once with other facts 
regarding the nature of the atmosphere, and the action of 
gravity, and so perceive at once its inferential necessity. 

(i) According to the view which has just been stated, necessity is 
not a property which belongs to any judgment in itself, but some- 
thing which arises through its dependence upon other judgments. 
In other words, necessity is always mediate, not immediate. This 
view, however, differs from a theory that was once generally re- 
ceived, and has some adherents, even at the present time, especially 
among thinkers who belong to the Scottish or ^common-sense' 
school. In dealing with the facts of experience, we always explain 
one fact by referring it to a second, and that second by showing its 
dependence upon some third fact, and so on. Thus the movement 
of the piston-rod in an engine is explained by the pressure of 
steam, and this is due to the expansive power of heat, and heat 
is caused by combustion of fuel, etc. We are thus referred back in 
our explanations from one fact or principle to another, without 
ever reaching anything that does not require in its turn to be 
explained. 



334 'J- he Main Characteristics of Judgment 

Now, it is said that this process cannot go on forever; for if it 
did there could be no final or complete knowledge; the whole 
system would be left hanging in the air. There must, therefore, 
it is argued, be some ultimate facts which furnish the support for 
the v/orld of our experience, some principle or principles which are 
themselves necessary and do not require any proof. That is, there 
must be certain propositions which are immediately necessary, and 
which serve as the final explanation for everything else. Now, it is 
clear that such propositions must be entirely different in character 
from the ordinary facts of experience, since their necessity belongs 
to their own nature, and is not derived from any other source. It 
had to be supposed, therefore, that they stood upon a different 
plane, and were not derived from experience. To explain the su- 
perior kind of certainty which they were assumed to possess, it was 
supposed that they were present in the mind at birth, or were innate. 
They have also been called necessary truths^ a priori truths^ and 
fundamental first principles, in order to emphasize their supposed 
distinction from facts which are derived from experience. 

When one regards knowledge as an internal process of growth 
or development, however, where each element plays its part, as do 
the members of a living body, the inadequacy of any view which 
looks for a mechanical basis for knowledge is apparent. What 
is present in experience is a moving system of functions, not a 
structure of fixed mechanical parts, such as exist, for example, 
in a building. 

§ 82. Judgment involves both Analysis and Synthesis. — 

The business of our thought is to understand the ways in 
which the various parts of the real world are related. And 
a judgment, as we have already seen, is just a single act of 
thought, — one step in the process of understanding the 
world. Now we ask: How does Judgment accomplish its 
task ? Does it proceed altogether by analysis, by pointing 



§ 82. Judgment involves both Analysis and Synthesis 335 

out the parts of which things are composed, or does it also 
employ synthesis in order to show how various parts combine 
in such a way as to form a whole ? Or is it possible for both 
these processes to be united in one and the same act of judg- 
ment ? 

Suppose that one actually makes the judgment for oneself 
(and does not merely repeat the words of the proposition), 
^ the rose has pinnate leaves.' What has taken place ? We 
notice, firstly, that a new property of the rose has been 
brought to light; a distinction, or mark, has been discovered 
in the content ' rose,' which was not seen to belong to it be- 
fore the judgment was made. So far, then, the process is one 
of analysis, of discovering the parts or distinctions of some- 
thing which is at first taken, as it were, in a lump. And this 
is a most essential element in all thinking. In order to know, 
it is absolutely necessary that the differences between the 
parts of things should be clearly apprehended, that we 
should not confuse things which are unlike, or fail to make 
proper distinctions. If we examine a number of instances 
where a real judgment is made, we shall find that this moment 
of analysis, or discrimination, is always present. Sometimes, 
indeed, analysis may not seem to be the main purpose of the 
judgment; but if one looks closely, one will always find in a 
judgment that elements which are unlike are held apart 
or discriminated. 

But let us look again at the same judgment, ' the rose has 
pinnate leaves.' It is not difficult to see that the discovery 
of something new in itself is only one part of what the judg- 
ment has accomplished. The judgment also affirms the union 
of this new discovery with the properties of what we call 
the rose. It is, therefore, from this point of view, an act of 



336 The Main Characteristics of Judgment 

synthesis. It asserts that the prickly branches^ fragrant 
flowers, feather-like leaves, and other distinctions are united 
in the one content which we call the rose. It does not stop 
with the mere assertion, ^ there is a mark or distinction,' but 
it afiirms that it is a mark of something, z.^. that it is united 
with other marks or properties to form a concrete whole. In 
other words, we may say that every judgment affirms the 
unity of the different parts, or aspects, of a thing; and this is, 
of course, synthesis. From this point of view, then. Judgment 
can be defined as a process of synthesis, just as we defined it 
above as one of analysis. 

But how, it may be asked, is it possible for a judgment to 
be both analytic and synthetic ? Are not these processes 
directly opposed to each other ? It is true that there can be 
no doubt that this is the case when we are dealing with ma- 
terial things: pulling things to pieces is the opposite of put- 
ting them together. When we are doing the one we cannot 
also be doing the other. But there is no such opposition 
between these processes when they go on in our minds. An 
illustration may make this clear. Suppose that one is trying 
to understand some piece of mechanism, say a watch; in 
order to be able to see how it goes, or judge correctly regard- 
ing it, two things are necessary. First, one must notice all 
the parts of which it is composed — the wheels of various 
sizes, springs, pins, etc. But, in the second place, one would 
not understand the watch until one saw how all the parts 
were united, how one part fits into another, and all combine 
together into one whole. We do not mean that these are two 
steps which take place in succession; as a matter of fact, the 
detection of the various parts, and the perception of their 
connection, go hand in hand. In the process of understand- 



§ 82. Judgment involves both Analysis and Synthesis 337 

ing the watch, we have both taken it to pieces and put it 
together again at one and the same time. Not really, of 
course, but in our thought. In the world of material things, 
as we have said, only one of these processes could go on at a 
time; but in every act of thinking, in every judgment, analysis 
and synthesis go hand in hand, and one has no meaning 
except with reference to the other. 

But the two moments or factors of analysis and synthesis, 
although present in every judgment, are not always equally 
prominent. The main purpose of the judgment usually falls 
on one side or the other. In a judgment like, ^ water can 
be divided into hydrogen and oxygen,' the main emphasis 
seems to be on the parts, and the assertion that these ele- 
ments are parts of a whole, though present, is only implied. 
But when one asserts, ' these springs and wheels together 
make up a watch,' it is the nature of the whole upon which 
the emphasis is laid, and the separation or discrimination of 
the parts is, as it were, secondary. It is not difficult to see, 
however, that the two moments of Judgment are present in 
both of these cases. The difference consists in the fact 
that at one time analysis, and at the other synthesis, is made 
the main purpose. 

It was at one time supposed that analytic and synthetic 
judgments were entirely different in kind from each other. 
An analytic judgment, it was said, is one in which the predi- 
cate is obtained by analyzing, or bringing to light, what is 
contained in the subject. Thus the judgment, ' all material 
bodies fill space,' is analytic; for the predicate (space-filling) 
is contained in the very notion, or idea, of a material body. 
All that is necessary in order to obtain the judgment is to 
comprehend the meaning of the subject. An analytic judg- 



338 The Main Characteristics of J^idgment 

ment, then, adds nothing to our knowledge. It merely 
enables us to bring to light and express what is contained in 
the ideas we already possess. A synthetic proposition, on 
the contrary, was defined as one in which the predicate was 
not already contained in the subject, but which added a new 
element or idea to it. ^This body weighs ten pounds,' for 
example, is a synthetic proposition, for one cannot obtain 
the predicate by analyzing the subject. The predicate adds 
a new fact which must have been derived from experience. 

(i) This view is, of course, fundamentally different from the ac- 
count of Judgment which we have just given. The absolute distinc- 
tion between analytic and synthetic judgments, like the theory 
that thought begins with concepts, arises, I think, from a substitu- 
tion of the spoken or written proposition for the judgment itself. 
In the proposition the subject seems to be the starting-point. We 
have a word or term which appears to be independent and capa- 
ble of standing alone. The question is, then, where shall we find 
the predicate? For example, in the proposition, 'iron is an ele- 
ment,' the subject stands first, and the predicate comes later. It 
seems possible then to say that we have first the subject 'iron,' and 
then join on to it the predicate 'element,' which has been obtained 
either by analyzing the subject, or from some previous experience. 
But the proposition, as a collection of words, must not be substituted 
for the act of judgment. Judgment, as we have already seen, is a 
single act of intelligence, which at once discriminates and brings 
into relation different aspects of the whole with which it is dealing. 
A mere subject by itself has not any intelligible meaning. If one 
hears the word 'iron,' for example, the word may call up certain 
mental images ; but by itself it is not a complete thought or fact in 
which we can rest. ' Well, what of it ? ' we say. The mind at once 
goes on to form some judgment like, 'this is iron,' or 'iron is heavy.' 
We cannot think a term without thinking something ojii. In short, 



§ 83. Constructing a System of Knowledge 339 

although the words which form the subject of a proposition are 
relatively independent, and can be used without the words which 
make up the predicate, in a judgment^ on the other hand, a subject 
is only a subject through its relation to a predicate. The propo- 
sition may be divided into parts, but the judgment is a single 
thought- activity, and cannot be divided (cf. § 79 ). 

§ 83. Judgment as Constructing a System of Know- 
ledge. — In this section we have not to take account of any 
new characteristic of Judgment, but rather to emphasize the 
part it plays in building up knowledge. As we have seen, 
Judgment works both analytically and synthetically: it dis- 
covers new parts and distinctions, and at the same time 
brings the parts into relation and thus builds up a w^hole. 
That is the law^ according to which thinking develops, and is 
just what we called differentiation and integration in a pre- 
vious section (§ 77). 

It is necessary here, however, to dwell upon the fact that 
each judgment may be regarded as a step in the process of 
building up a system of knowledge. The emphatic word 
here is ' system,' and we must be perfectly clear about its 
meaning. A system is a whole which is composed of va- 
rious parts. But it is not the same thing as an aggregate 
or heap. In an aggregate or heap, no essential relation 
exists between the units of which it is composed. In a heap 
of grain, or pile of stones, one may take away any part with- 
out the other parts being at all affected thereby. But in a 
system, each part has a fixed and necessary relation to the 
whole and to all the other parts. For this reason we may say 
that a building, or a piece of mechanism, is a system. Each 
stone in the building, each wheel in- the watch, plays a part, 
and is essential to the whole. In things which are the result 



340 The Main Characteristics of Judgment 

of growth, the essential relations in which the parts stand is 
even more clearly evident. The various parts of a plant or 
an animal have their own functions, but at the same time 
they are so necessary to one another that an injury to one is 
an injury to all. We express this relation in the case of living 
things by saying that the parts are organic to one another. 
And, in the same way, it is not unusual to speak of society as 
an organism, in order to express the fact that the various 
individuals of which it is composed are not independent 
units, but stand in necessary relations to one another, and 
are all mutually helpful or hurtful. 

We have said that Judgment constructs a system of know- 
ledge. This implies, then, that it is not merely a process 
of adding one fact to another, as we might add one stone to 
another to form a heap. Judgment combines the new facts 
with which it deals, with what is already known, in such a 
way as to give to each its own proper place in relation to and 
interdependence with the others. Different facts are not 
only brought together, but they are arranged, related, sys- 
tematized. No fact is allowed to stand by itself, but has to 
take its place as a member of a larger system of facts, and 
receive its value and meaning from this connection. Of 
course, a single judgment is not sufficient to bring a large 
number of facts into relation in this way. But each judg- 
ment contributes something to this end, and brings some 
new fact into relation to what is already known. Even in 
a simple judgment like, ^ that was the twelve o'clock whistle,' 
the constructive or systematizing work accomplished is 
evident. The auditory sensation, which in itself, as a mere 
sound, was not a piece of knowledge at all, is interpreted in 
such a way as to find a place in the system of experience. 



§ 83. Constructing a System of Knowledge 341 

One may appreciate what part the judgment really plays by 
remembering how the sound appeared before one was able 
to judge. There may have been at first a moment of be- 
wilderment — ' What does this mean ? ' one asks. In the 
next moment the judgment is made: ' It is the twelve o'clock 
whistle.' That is, our thinking has constructed a meaning 
for it, and brought it into relation with the rest of our know- 
ledge. 

(i) Every new experience is thus brought into relation with the 
facts which we already know, and is tested by them. It has to find 
its place in the system of knowledge — to join itself to v/hat is already 
known. If this is impossible, if what claims to be a fact is entirely 
opposed to what we already know on the same subject, it is usually 
declared to be false. Thus, we would refuse to believe that some 
person whom we know well and respect was guilty of theft; for it 
would be impossible to connect such conduct with what we already 
know of his character. And, similarly, we find it impossible to 
believe, even although we have the evidence of our senses, that the 
conjurer has actually performed what he professes; for to do so 
would often be to reverse entirely our conception of natural laws. 
It must not be forgotten, however, that the existing system of know- 
ledge, which seems to serve as the standard and test of new facts, is 
itself undergoing constant modification through the influence of 
these facts. As new experiences are brought into connection with 
the existing body of our knowledge, there is a constant rearrange- 
ment and readjustment of the latter going on. Usually this adjust- 
ment is slight, and takes place almost imperceptibly. But, in some 
cases, a single fact may be so significant as completely to transform 
what seemed to be the accumulated knowledge of years. The 
experiment which Galileo made by dropping balls of different 
Vv^eight from the tower of Pisa, made it impossible to hold any longer 
the old theory — which seemed as certain as anything well could be 



342 The Main Characteristics of Judg?nent 

— that the velocity with which bodies fall is proportional to their 
weight. Again, if theft were actually proved against the man we 
respect, that single fact might be sufficient to force us to give up 
everything which we supposed that we knew about his character. 
(2) We have said that judgment is the process by which know- 
ledge grows into a system. It is by judging or thinking that we 
attempt to bring the various parts of our experience into relation 
with one another. The degree to w^hich this has been done is the 
measure of our intellectual development. The knov/ledge of the 
uneducated and unthinking man, like that of the child, is largely 
composed of unrelated fragments. It is an aggregation, not a 
system of facts. The facts which go to make it up may quite well 
be contradictory, but this contradiction is not seen because no 
attempt is made to unite them. There is, of course, no human 
experience which is entirely systematic, or which has been com- 
pletely unified. Even those who have thought most deeply find it 
impossible to fit together exactly knowledge gained from different 
fields, and from different sciences. The facts of one science, for 
example, may seem to stand by themselves, and not to have any 
relation to the facts derived from another science. Or there may 
appear to be a conflict between the results of physical sciences, 
and the truths of moral philosophy and religion. But the ideal 
always remains, that truth is one and indivisible, and that it must 
be possible ultimately to harmonize all facts in one all-embracing 
system of judgments (cf. Ch. XXVI.) . 

REFERENCES 

B. Bosanquet, The Essentials of Logic, Lecture II. 
'^ ^' Logic, Vol. I., pp. 97-103. 

C. Sigwart, Logic, § 18. 



CHAPTER XXIII 

THE LAWS OF THOUGHT 

§ 84. The Law of Identity. —We found (§ 78) that Judg- 
ment is the simplest form of thinking. And, in the last chap- 
ter, we were engaged in studying its main characteristics, 
and becoming acquainted with its mode of operation. The 
essential nature of the thinking process, therefore, has already 
been stated, though we have not traced the mode of its devel- 
opment, or shown its application to the various problems 
of experience. But, before undertaking this, it is necessary 
to turn aside to consider another problem. In nearly all 
books dealing with logic one finds a statement of three funda- 
mental laws of thought which differ greatly, in form at least, 
from what we have so far learned regarding the nature of 
Judgment. These laws are so well known by name, and 
yet so ambiguous in their mode of statement, that it seems 
well to try to decide what meaning to apply to them. For 
their interpretation will be found to furnish further illustra- 
tion of the nature of Judgment, and will thus throw light on 
the discussions of the last chapter. The laws of Thought 
are usually regarded as axioms, or propositions which require 
no proof, rather than as laws descriptive of the nature of 
thought in any special circumstance. In this sense, they are 
supposed to be the foundation of all logic, since they are pre- 
supposed in all thinking. 

The first of these laws, or axiomatic principles, is that of 
Identity. * Whatever is, is; ' ' Everything remains identical 

343 



344 The Laws of Thought 

with itself ; ' ' A is A.' These are some of the forms in which 
the law is usually stated. What is meant by these statements 
is, that in all argument, we necessarily assume, if we are 
to reason at all, that each thing possesses a permanent char- 
acter, and does not pass now into this, now into that at ran- 
dom. If any knowledge is to be possible at all, the character 
of things must remain fixed. Socrates is always to be Soc- 
rates, and iron, iron. Things are also constantly undergoing 
changes. The law of Identity, of course, does not deny this, 
or declare that the changes are unreal. It rather presupposes 
the changes; but goes on to affirm that there is an identity 
persisting in and through the difference. Identity means 
identity in difference: it is this which all our judgments as- 
sert. Socrates changes, or is different from day to day and 
from year to year. But he also remains identical with him- 
self; he is in his old age the same Socrates who talked with 
Parmenides in his youth and fought at Potidaea when in 
middle life. Identity, then, does not affirm the static and un- 
changeable character of things and thoughts; but that 
there is continuity in change, in virtue of which things main- 
tain themselves and are capable of being known as parts of 
a coherent system. Every one assumes as much as this in 
every judgment he makes, though he may not himself be 
conscious of it (cf. § 9). 

Another interpretation of this principle was, however, 
offered by Boole and Jevons, who developed what is known 
as the Equational or Symbolic logic. According to these 
writers, the law of Identity expresses the fundamental nature 
of Judgment, and is to be interpreted as a statement of an 
exact and bare identity. That is to say, every judgment 
is the expression of an identity between the subject and the 



§ 84. The Law of Identity 345 

predicate. The judgment, ^ New York is the largest city in 
America/ is simply a case of a is a. It expresses the fact, 
that is, that New York and the largest city in America are 
identical. ^ Iron is a metal,' is another example of the same 
principle. It may be written: iron = metal. And, since 
the copula may often be ambiguous, it will be better to discard 
it in working out arguments, and adopt, in its place, the 
sign of equality. 

Judgment, from this point of view, is thus simply an equation, 
and may be written as such. Furthermore, the conclusion 
of a series of logical premises may be obtained by a process 
similar to that employed in working algebraic equations. That 
is, we can substitute for any term in a judgment, its equivalent, 
or the value which it has in another judgment. This method 
Jevons calls ^ the substitution of similars,' which he maintains 
is the fundamental principle of all reasoning. 

If, now, we employ letters to symbolize the terms of the 
propositions, it is claimed that we can work out any argu- 
ment by the equational method. Take the argument, 

All metals are elements. 

Iron is a metal. 

Therefore iron is an element. 

Now represent metal by M, iron by I, and element by E. 
Then the argument in equational form will be, 

M = E (i) 

I = M (2) 

and by the substitution in (i) of the value of M in (2) we get 
I = E, the required conclusion. 

Or, we may illustrate this method by a somewhat more 
complex example which is also taken from Jevons : ' Common 



346 The Laws of Thought 

salt is sodium chloride, which is a substance that crystallizes 
in cubical form; but what crystallizes in cubical form does 
not possess the power of double refraction.' The conclusion 
of this argument may be found by letting A = Common 
Salt, B = Sodium Chloride, C = something which crys- 
tallizes in cubical form, and D = something which possesses 
the power of double refraction. The negative of any of these 
terms will be expressed by the corresponding small letters. 
The argument may now be expressed: — 

A = B (i) 

B = C (2) 

C = d (3) 

By substitution of the value of C in (2) we get, 

B = d . (4) 

And substituting here the value of B in (i), 

A = d. 

Giving to these symbols their meanings, we get the result 
* common salt does not possess the power of double refrac- 
tion,' which is the conclusion of the argument. 

Of course, in simple arguments like those we have been 
examining, there is nothing gained by the use of symbols, 
and the representation of arguments in this form. But 
when the various terms employed are much longer and more 
complex, simplification may be attained in this way. Va- 
rious other symbols have also been used to express the rela- 
tion of the various terms to one another, and a symbolic 
logic has been developed which follows very closely the pro- 
cedure of algebra. B y following closely the methods of mathe- 
matics, but seeking to obtain a more general form of express- 
ing the relations than mathematics employs, results have 



§ 84. The Law of Identity 347 

been obtained that are of much interest and which may prove 
valuable.^ 

It is, however, as a theory of the meaning of Judgment that 
we are interested in this mode of interpreting the law of 
Identity. We have seen that it works fairly well in practice, 
and therefore cannot be wholly false. But there are cer- 
tain forms of reasoning in which it will not work. We can- 
not get the conclusion by the equational method in an example 
like the following: ' B is greater than A, C is greater than B, 
therefore C is still greater than A.' 

This practical objection being left out of account, we have 
to ask whether an equation represents fairly the nature of 
Judgment. Does a judgment express merely the identity 
of subject and predicate ? And if so, what hind of identity 
is referred to ? In mathematical reasoning, the sign of 
equality expresses the identity of quantitative units. When 
one says, 2+3 = 5, the meaning is that the number of units 
on each side of the equation is identical. And, similarly, 
the assertion that a parallelogram = 2 triangles with the 
same base and of the same altitude as itself, expresses the 
fact that, in the two cases, the number of units of area, square 
feet, square yards, etc., is the same. In mathematics, the 
equation declares that the quantitative relations of its two 
sides are identical. It does not assert that the two things 
compared — the triangle and one-half the parallelogram, 
for example — have the same qualities, or are exactly the 
same in all respects. Now, if we extend the use of the sign 

^ The clearest statement of the aims and methods of the Equational 
Logic may perhaps be obtained from Jevons, The Principles of Science, 
Introduction. Cf. also G. Boole, An Investigation of the Laws of Thought, 
London, 1854; and A. T. Shearman, The Development of Symbolic Logic, 
London, 1906. 



348 The Laws of Thought 

of equality, it must take on a new meaning. It is clear that 
in a judgment like ^ iron == metal,' there is no reference at 
all to quantitative relations. We are not asserting that the 
number of units in the two terms is identical. What, then, 
does the sign of equality express in such a case ? 

The answer is not difficult, say those who hold this theory. 
The sign of equality in such cases expresses absolute identity; 
the entire and complete sameness of subject and predicate. 
The proposition, ' mammals = vertebrates,' asserts that 
mammals and vertebrates are one and the same thing. But 
that statement in its present form is not true: the class 
mammal does not completely correspond with the class 
vertebrate. To make it exact, reply those who uphold the 
equational form, one must qualify or limit the predicate 
and write the proposition, ^ mammals = some vertebrates.' 
But, even so, we may urge, the form of the judgment is still 
defective. In the first place, it does not correspond to the 
model a = a. For one side, ^ mammal,' is clearly marked 
off, while the other is indefinite and vague. And, secondly, 
just because of its vagueness, it is not a satisfactory piece 
of knowledge. To obviate these objections, one must go 
further and write, mammals = mammalian vertebrates. 
At last the judgment seems to correspond to the type, a =^ a. 
But a new difficulty arises. Has not the judgment lost all 
its original meaning and become a mere tautology ? There 
seems to be no escape from the following dilemma: either 
there is some difference between subject and predicate, and 
the judgment is therefore not in the form a = a, or the 
judgment is tautologous and expresses nothing. The view 
of the equational logic that Judgment affirms the entire iden- 
tity of subject and predicate refutes itself. The form a = a 



§ 84. The Law of Identity 349 

cannot be regarded as the type to which all judgments con- 
form. 

But there must be some kind of identity between the parts 
of a judgment. In one sense, we do seem to declare that the 
subject and predicate are identical when we say, ^ iron is a 
metal.' As we have seen, however, if these terms are merely 
identical and nothing more, the judgment loses all meaning. 
We are forced to the conclusion that every judgment affirms 
both identity and difference, or that there is identity running 
through and underlying the diversity. But is not this a 
paradoxical statement ? When we affirm identity, does not 
this imply the absence of all difference ? If a is a, how can 
it at the same time be something different from itself ? 

And yet this is just what every judgment which has any 
meaning affirms. ' Iron is fusible.' ^This table is made of 
oak.' ' The sword is rusty with age.' In all these judgments 
there is an assertion of the unity of different properties or 
parts in one whole. A is B, and yet does not cease to be A, 
is rather the type of judgment than a is merely or abstractly a. 
It is worth noticing that this view of the matter corresponds 
with the account of Judgment already given. We saw that 
Judgment constructs a system of knowledge by showing 
that various things, which seem at first unrelated, are yet con- 
nected by an underlying unity. Knowledge is always the 
synthesis or union of different parts or diff'erent properties 
in a common identity. And each judgment, as an element of 
knowledge, displays the same essential structure which be- 
longs to knowledge as a whole. It involves, as was shown 
in § 82, both analysis and synthesis, and declares the one- 
ness or identity of a number of properties or parts, without 
at the same time losing sight of their distinctness. 



350 The Laws of Thought 

Let us now sum up our discussion of the law of Identity. 
When rightly understood, as we have seen, it does not affirm 
that a can only be bare a, that the subject and predicate are 
absolutely identical. As a law of thought, it expresses the 
fact that Judgment brings together differences, ix,^ different 
things and qualities, and shows that they are parts of one 
whole or unity. That is, judgraent reveals the underlying 
unity or identity which is present in the midst of variety. 
This law also states another characteristic of Judgment 
which we have already emphasized. This is what we have 
called the universality of Judgment (§ 80). It is to judg- 
ments, and not to concepts or terms, as has sometimes been 
supposed, that the law of Identity properly applies. What 
it affirms in this connection is simply that Judgment claims 
to be true, and hence is identical at all times and for all per- 
sons. It cannot be true for you and false for me that, ^ iron 
is a metal,' and the judgment must at bottom mean the same 
for all men. Truth is not a matter of individual taste, but 
every judgment which is true has a permanent character or 
identity of meaning belonging to it. 

§ 85. The Law of Contradiction. — The law of Contra- 
diction is the second of the so-called laws of thought. It is 
usually stated as follows: it is impossible for the same 
thing both to be a, and not to be a, or, a is not not-a. It is 
evident that this lav/ states in a negative form the same char- 
acteristics of thought as the law of identity. Indeed, it was 
in this form that the principle was first laid down by Aris- 
totle. ''It is impossible," he says, '' that the same predicate 
can both belong and not belong to the same subject at the 
same time, and in the same sense." ^ We cannot assert 

^ Metaphysics^ Bk. III., Ch. IV. See also the remaining chapters of the 



§ 85. The Law of Contradiction .351 

that Socrates is both wise, and not wise. Truth is not, as 
the Sophists supposed, a matter of taste or convenience, but 
must be consistent with itself. If a judgment affirms that 
*' iron is a metal,' it at the same time excludes the assertion 
that it is not a metal. There is a fixity and permanence 
about judgments which prevents them from changing into 
anything else. And it is just this permanence which we have 
already called the universality of Judgment, which the law 
of Contradiction expresses in a negative form. 

The law of Contradiction has, however, sometimes been 
interpreted in such a way as to make it equivalent to the as- 
sertion of abstract or bare identity which we found in the 
Equational logic. That is, the statement that it is impossible 
for any judgment to unite a and not-a may be taken to mean 
that it is impossible to assert the unity of a and anything 
different from a. But, as we have seen, this is exactly 
what we do in every judgment which is more than a tautol- 
ogy. The law, then, does not forbid the union of differences 
in one judgment, but of contradictories^ or of what would 
destroy the integrity of the judgment and render it unmean- 
ing. If the law is to hold true of Judgment, not-a must not 
be taken as equivalent to anything which is different from 
a, but as signifying what is opposed or contradictory to a. 

It is not by any means easy to decide what things are merely 
different, and therefore compatible with one another, and what con- 
tradictory or opposed. Logic can g\N^ no rule which may be applied 
in every case. If experience shows that two things, or two proper- 
ties, are at any time united, we say that they are merely different 
from each other; if they have never been found in conjunction and 

same book for Aristotle's demonstration that all thought presupposes such 
a principle. 



352 The Laws of Thought 

we are not able to conceive how their union could take place, we 
call them opposites or contradictories. It is worth noticing, too, 
that no terms are in themselves contradictory, except those which 
are in the form a and not-a^ wise and not-wise. But they become 
contradictory and exclude each other when they claim to occupy 
the same place in some particular system of facts. Thus ^ maple' 
and ^ oak ' denote trees of a different variety, which are, however, so 
little opposed that they may exist side by side. If both these terms 
were applied to the same tree, however, they would become con- 
tradictory. By claiming to stand in the same relations, these 
terms become rivals, as it were, and exclude each other. But a 
knowledge of the particular facts involved is always necessary in 
order to determine whether or not two assertions are really incom- 
patible. 

§ 86. The Law of Excluded Middle. — The third law is a 
corollary from what has just been said in the last section. 
There is no middle ground, it declares, between contradic- 
tories. A is either b or not-b. To affirm the one is to deny 
the other. When we have real contradictories, — i.e., w^hen 
not'b is not merely something different from &, but some- 
thing which excludes it, — every judgment is double-edged, 
and both affirms and denies at the same time. To deny 
that the throw of a penny has given heads, is to assert that 
it has fallen tails. As we have seen, however, logic affords 
no rules for deciding when things do thus stand in the rela- 
tion of mutual exclusion. The law of Excluded Middle 
states only that where this relation does exist, every proposi- 
tion has a double value, and both affirms and denies at the 
same time. It requires special knowledge of the particular 
facts in each case to enable us to decide what things are 
thus opposed to one another. There is no logical law by 



§ 86. The Law of Excluded Middle 353 

means of which things may be divided into two contradictory 
or exclusive groups or classes. 

It is important to notice that all of the judgments which 
we use in everyday life are to some extent double-edged. 
That is, they contain, besides what is directly affirmed, some 
implication or counter statement. For example, to say, 
* that object is red,' is implicitly to deny that it is blue, or any 
other colour. The statement, ' A never looks at a book,' 
carries with it certain implications which may perhaps be 
held in mind as a series of hypotheses: ^ Is he then too busy, 
or sick, or simply indifferent ? ' In almost any field where 
we have any systematic knowledge, we can limit pretty defi- 
nitely the number of possibilities — a must be either 5, or c, 
or d. In such cases, to affirm that a is 6, is of course to deny 
implicitly c and d; and conversely, the denial of any one pos- 
sibility, as ^, enables one to assert that a is 6 or d. In ordi- 
nary conversation, misunderstandings and misconceptions 
frequently arise because neither party is fully aware of all 
the possible cases and the relation between them. It is very 
difficult, however, to make a statement which will have 
no counter implications. If one says, ' this railway system 
does not employ steam power,' the proposition seems to jus- 
tify the question : ^ Does it then use electricity or compressed 
air ? ' We should feel that it was a mere quibble if the per- 
son who made the statement should reply : ^ I did not say 
it employed any kind of power.' ^ There are some small 
errors in this paper,' would ordinarily be taken to imply the 
counter proposition, ^ the paper contains no serious errors.' 
It is clear that it is only when one's knowledge becomes 
systematic^ — i.e.^ when one knows the relations in which all 
the facts in the field under consideration stand to one an- 
2 A 



354 T^^^^ Laws of Thought 

other, — that one can be fully aware of what is really implied 
in each assertion or denial (cf. §§ 26, 83). It is, however, 
of fundamental importance to understand that in its work 
of defining the nature of things thought works with a double- 
edged tool. Omnis definitio est negatio, wrote Spinoza: to 
define is to exclude or eliminate. But as we have shown, 
the process of elimination is not merely positive but yields 
positive results. 

These so-called Laws of Thought, when read in relation 
to one another, may then be interpreted as expressing the uni- 
versal Postulate of our intelligence, that experience shall be 
capable of being organized as a system. If there were 
nothing but Identity — if everything were identical with 
everything else — there could be no universe and no know- 
ledge. Nor would any knowledge be possible if things were 
merely different : if there were no common space and time, 
no common natures and laws of relationship, the world would 
be nothing but a disorganized chaos, without form and void. 
Finally, experience would not be possible as a coherent sys- 
tem if each fact had not some particular place or bearing, in 
such a way that one affirmation or denial carried others with 
it. Reality exists as a system of mutual implications and 
exclusions. It must so exist if it is to be knowable. That 
Reality is knowable by Intelligence, may, then, be regarded 
as the ultimate postulate of knowledge, and this, as we have 
seen, is the final interpretation to be given of the Laws of 

Thought. 

REFERENCES 

F. H. Bradley, The Principles of Logic, pp. 131-154, 343-360. 

B. Bosanquet, Logic, Vol. II., pp. 207-212. 

W. S. Jevons, The Principles of Science, Introduction. 



CHAPTER XXIV 

TYPES OF JUDGMENT 

§ 87. Judgments of Quality. — We have hitherto been 
considering the nature of Judgment in general, and have 
learned something regarding its main characteristics. It is 
now necessary to examine briefly some of the more important 
forms or types of Judgment. In § 5 1, we spoke of the different 
forms or conceptions in terms of which things are brought into 
relation as * Categories.' This chapter might therefore have 
been entitled, ^The Main Categories of Thought/ as it is with 
certain typical ways in which things are related that we are 
here concerned. We shall begin with very simple and elemen- 
tary ways of judging, and afterwards consider some of the 
more complex types. In this way, we shall see the nature 
and structure of Judgment illustrated at different levels of 
thought. We also hope to show, by this review of types, 
that there are no arbitrary divisions in the process of thinking, 
but that the lower forms of Judgment gradually develop into 
the higher in accordance with the general law of evolution. 
It is, of course, impossible to carry out at present this plan in 
detail, for that would be to give a complete history of the 
development of thought. It will be necessary for us to take 
long steps, and content ourselves with a general view of the 
relation of the various stages in the development of Judgment. 

The first efforts of intelligence to understand the world 
take the form of judgments of Quality. At a low stage of 

355 



356 Types of Judgment 

mental development, it is the simple qualities of things 
which force themselves on attention. The young child, for 
example, takes notice only of the most striking qualities of 
things. His judgments are very vague and indefinite, and 
take account only of some prominent quality of things. That 
is, there is in them no discrimination of the various parts and 
relations of the objects, but they express merely a general 
impression based upon some striking quality. Thus it has 
often been noticed that the child calls every man ^papa,' 
and any light, of whatever size, the moon. A little boy, 
known to the author, used to call Sisters of Charity crows, on 
account of the colour of their dresses. The objects as he 
apprehended them were simply black, and nothing more. 
His intelligence rested in the qualitative total impression: 
the various parts, with their diverse relations, which he 
afterwards learned to know and distinguish, did not at that 
time exist for him. 

It is perhaps impossible to find in the experience of an 
adult any judgments which deal entirely with simple qualities, 
and which take no account of the numbers, or even to some 
extent of the relations, of the parts. But we can find examples 
of judgment where the qualitative aspect is much the most 
prominent — where indeed the quantitative and more com- 
plex relations are scarcely noticed at all. ^This is green,' ^that 
is a strange odour,' ^ there is something a long way off,' — 
all these seem to be judgments of quality or general impres- 
sion, and to involve scarcely any other element. This is, 
also, the easiest kind of judgment to make, the judgment which 
involves least mental effort, and which notices only the most 
evident, and, as may be seen, the most superficial, aspect of 
things. It is evident that such judgments belong to a lower 



§ ^7' Jttdgments of Quality 357 

stage of thinking than those which imply analysis and per- 
ception of quantitative relations. Compare, for example, 
^ this is very large,' with, ^ this tree is made up of roots, trunk, 
branches, and leaves'; or ^this is green,' with, 4his leaf 
is divided into two parts by a rib running through the centre.' 
The first judgment in each pair obviously involves much less 
intellectual work than the latter. The judgment of simple 
quality accordingly is, as we have said, the starting-point of 
thought. It is with this kind of thinking that the knowledge 
of the child begins. And, before the savage learns to count, 
i,e, to distinguish and enumerate the parts of the objects with 
which he deals, his judgments must necessarily belong to this 
same type. 

It must never be forgotten, however, that simple judgments 
of quality are really judgments; that is, they are not given to 
the mind from any external source, but are the products of 
its own activity. A judgment, as we have already pointed 
out (§ 78), implies a reaction on the part of the mind on what 
is presented to consciousness through the senses. It dis- 
tinguishes and puts together the material which sense pre- 
sents in such a way as to perceive its significance — what it 
really amounts to — as a piece of knowledge. This act of 
interpretative intelligence has gone, however, but a little 
way in the type of judgment with which we are dealing. 
But even in a vague qualitative judgment like, ' there is some- 
thing black,' the essential characteristics of Judgment can be 
already distinguished. For it presupposes at least some 
analysis or discrimination of the black object from the rest of 
the environment, and of the black colour from other colours. 
And the judgment, ^something is black,' has made at 
the same time a beginning in constructing this vague some- 



358 Types of Judgment 

thing into a system of qualities, or into a thing that is known. 
The other quahties and relations are as yet wrapped up in the 
indefiniteness of the ^something.' In spite of its indefinite- 
ness, however, the latter plays the part of a permanent centre 
or identity. It is the whole from which the quality of black- 
ness has been separated out, and to which it is again attached. 

Our thought, however, is not satisfied with a knowledge of 
the general qualities of things, but pushes farther its work of 
analysis and construction. In this way, it begins to distin- 
guish the various parts of objects, and to compare one with an- 
other. We not only judge that ^ the grass is green,' but go 
further and say ^ this piece is dark green, and that light green.' 
The indefinite judgment, ^this cane is heavy,' is no longer 
satisfactory, and is replaced by, ' this end of the cane is much 
heavier than that.' And when this stage is reached, judg- 
ments of Quality are already passing into the next higher 
type, judgments of Quantity. For the element of comparison, 
which is already contained in these judgments, is the basis of 
counting, measuring, and all quantitative determination. In 
advancing from the simple apprehension of quality, to the 
stage where it takes note of, and compares, the degree or 
intensity which the same quality manifests in different instances, 
intelligence has entered upon a path which leads directly to 
judgments of quantity. To distinguish parts, to regard things 
as degrees or instances of a common quality, is at once 
to suggest the quantitative process of counting and measure- 
ment. 

§ 88. Judgments of Quantity. — It is very difficult, as we 
have seen, to draw a hard and fast line between quality and 
quantity. Indefinite judgments of general impression which 
do not imply any comparison, seem always to be qualitative 



§ 88. Judgments of Quantity 359 

rather than quantitative in character. This is true, I think, 
of judgments hke, ' this object is very large/ ' there was a great 
flock of sheep in the field.' In such cases, the interest does 
not seem to be quantitative at all; i.e, there is no effort 
made to determine how many units or parts there are in the 
whole about which the judgment is made. But the general 
impression of size or number is apprehended and judged of 
at the same level of intelligence, and in the same vague way, 
as the simple qualities with which we dealt in the last section. 
It is by means of such a general qualitative impression that 
the savage who cannot count beyond five, is able to distinguish 
between six and some larger number. And we cannot im- 
agine that the shepherd's dog learns that some of the sheep are 
missing by any process of counting. We must suppose that 
the general quahtative impression made by the smaller flock 
is different from that made by the larger, and that there has 
been no real counting or estimation of number in the case. 

But quantitative judgments proper belong to a higher stage 
of intelligence than do those which have just been described. 
Indefinite judgments, like ' this is very large,' or, ' there are a 
great many stars in that group,' are not satisfactory pieces of 
knowledge. We accordingly set ourselves to get more exact 
information about the parts which compose the wholes, or to 
analyze and distinguish. The first step in this process leads 
to Judgments of Enumeration. If the whole which is analyzed 
is composed of homogeneous parts, the judgments of enumera- 
tion take the form of simple counting. ^There are one, two, 
three, . . . twenty men in this company.' Where the parts 
are not of the same kind, however, a separate name may 
have to be given to each. ^This plant is composed of root, 
stalk, leaves, and flower.' 



360 Types of Judgment 

But exact quantitative knowledge requires us to do more 
than enumerate the parts of which a whole is composed. We 
must go on and weigh or measure them. There is of course no 
essential difference between weighing and measuring, so that 
we may call all judgments which express the result of this 
process Judgments of Measure, It is worth noting that judg- 
ments of this class are not so simple and direct as may ap- 
pear at first sight. When we measure, we express the relation 
of the parts with which we are dealing to some common unit 
or standard. The judgment, 'this tower is 200 feet high,' 
means that if the tower is compared with a foot-rule, it will be 
found to be 200 times as long. It really, then, involves a pro- 
portion, and might be expressed: — tower : foot-rule = 200 : i. 

The point which it is important to notice is that all measure- 
ment is the result of comparison. In the first place, some unit 
is more or less arbitrarily selected. Then the judgment states 
simply the relation between this unit and the object measured: 
one is contained in the other once, or twice, or ten times. 
The quantitative determination thus obtained is accordingly 
merely relative. That is, it does not belong absolutely, and 
in its own right to the object measured, hut indicates the rela- 
tion of that object to something else. 

For this reason, it may seem that quantitative relations 
tell us nothing regarding the real nature of objects, and that 
to discover what the latter are in themselves, we shall have to 
return to the point of view of quality. But we have seen that 
simple judgments of quality yield a very vague and unsatis- 
factory kind of knowledge. Moreover, we should discover, 
by thinking the matter out, that even qualities always imply 
a reference to one another, and are no more absolute than 
quantities. 



§ 88. Jiidgnie7it of Quantity 361 

In order to obtain more satisfactory knowledge regarding 
things, we shall have to go forward to a higher type of judg- 
ment, rather than backward to quality. But the importance 
of quantitative determination for exact knowledge must not 
be overlooked. By means of measurement, things are re- 
duced to common terms, as it were, and thus a basis of com- 
parison is afforded where it would otherwise be impossible. 
To reduce everything to such a common measure is the busi- 
ness of the physico-mathematical sciences. Everything has 
a quantitative value, and can be expressed mathematically in 
terms of some unit or standard, as, for example, the unit of 
heat, or of pressure, or the electrical unit. It was this ten- 
dency to count and measure and weigh things which es- 
tablished the body of exact knowledge which we call science. 
And in almost every field, knowledge increases greatly, both 
in extent and exactness, as soon as it is found possible to re- 
duce the phenomena under investigation to a common measure, 
and to express their relations by means of mathematical 
formulas. 

It is a great step in advance to be able to compare things as 
quantities, and to express their relations in terms of number. But 
judgments of quantity are not entirely satisfactory ; they are, as has 
already been noticed, merely relative in character. Moreover, from 
a quantitative point of view, each thing is equivalent to the sum of 
its parts. When the parts have been enumerated and measured, 
the value of the whole is obtained by addition. But it is scarcely 
ever possible to represent adequately the nature of a whole in this 
way. So long as we are dealing with a piece of inorganic matter, 
the method of regarding the sum of the parts as equivalent to the 
thing, generally gives good results and leads to no difficulty. But it 
is quite different when the whole question belongs to something 
which has life and consciousness. In such cases, we have what has 



362 Types of Judgment 

already been called an organic whole (§ "^i). Now, it is clear that 
the principle of quantity, which can only add and subtract, is in- 
sufficient to represent completely the nature of an object of this kind. 
It has no means of representing the individuality or real whole, 
which rather constitutes the parts, than is constituted by them. 
That is, to understand such objects, we shall have to take a new 
point of view, and begin with the whole rather than with the parts. 
From the point of view of quantity, the nature of the whole is dis- 
covered by adding together the parts ; while in objects which possess 
an individuality of their own, there seems to be a central principle 
to which the parts are subordinated, and in relation to which alone 
they can be understood. The type of judgments which deal with 
such objects we shall have to discuss in § 90. 

§ 89. Judgments of Causal Connection. — Another class of 
judgments used in building up knowledge, may be called 
judgments of Causal Connection. They undertake to show 
how the various changes which go on in things are connected 
causally with other things or events. This type of judgment 
— leading as it does beyond the particular object to a know- 
ledge of the ways in which objects are connected — seems 
to belong to a higher stage of mental development than those 
which merely take note of quality and quantity. This does 
not mean that we never look for causes until the qualities and 
quantities of things have been discovered. Nor is it true that 
any causal judgment, however vague and unsatisfactory, is 
higher than any judgment of quality or quantity whatsoever. 
But, in the beginnings of knowledge, one may say, thought 
does not travel outside the particular object to show the con- 
nections of the latter with anything else. And, beginning in 
this way, it seizes first upon quality and quantity; which seem 
to belong to things in themselves. We have seen, however, 
that as a matter of fact judgments of quantity involve com- 



§ 89- Judgments of Causal Connection 363 

parison, and so a reference of one thing to another, though 
that reference is not usually made consciously or explicitly. 
In this form of judgment, the reference does not seem to 
imply any objective relations of the things compared. If, for 
example, I say that this desk is twice as long as my arm, this 
relation appears quite external and accidental : the nature of 
the one remains independent of that of the other. But, 
when we judge that one thing is causally connected with an- 
other, the accidental relation expressed in quantity has be- 
come essential and objective, indicating a closer relation- 
ship between things than is expressed in a quantitative 
comparison of the judgment. 

The word ^ cause ' has been used in a great many senses, 
and its various meanings have given rise to a great deal of 
discussion. That every event must have a cause, was for- 
merly regarded as an innate truth, or a priori proposition. 
We have seen, however, that we do not come into the world 
with any ready-made stock of knowledge. All knowledge, we 
have often repeated, is the result of the mind's own judging 
activity. The so-called law of causation (every event must 
have a cause) must therefore express the fact that thought 
does connect things as causes and effects. Intelligence is not 
satisfied to take things in isolation; it tries to gain an insight 
into the ways in which they are connected, to discover what one 
has to do with another. And this is just the characteristic of 
thought which was emphasized in § 83. Judgment, it was 
there said, is a process of constructing a system^ of showing how 
the various parts of knowledge fit into one another, and are 
mutually dependent upon one another. The tendency of 
thought to connect things causally, then, is simply one of the 
fundamental forms in which its tendency towards a system 



364 Types of Jiidgment 

expresses itself. In employing the causal category, judgment 
has become more explicit and conscious of itself than it was 
in quality and quantity. 

It is interesting to note some of the more important 
changes which take place in the principle of causal explana- 
tion at different stages in the development of knowledge. 
The child and the savage regard all changes and events which 
take place in the natural world, as due to the agency of livkig 
beings. These beings are represented as more or less similar 
to men, and as endowed with human passions and emotions. 
Thus we say that the earliest kind of explanation is essentially 
anthropomorphic. This word is derived from av6p(DTro^j a 
man, and fJiopc^rj, shape or form, and hence is used to describe 
the way of representing either a spiritual being, as, for example, 
the Deity, or natural forces like fire, wind, etc., in human 
form. It is probably true that at a very early stage in the 
development of both the individual and the race, every object 
was supposed to have life. Or, perhaps, it would be truer to 
say that the young child (and the same would be true for the 
savage on a low plane of intelligence) has not yet made the 
distinction between animate and inanimate objects, but 
vaguely regards everything as like himself. This stage is 
usually known as animism, because each object is supposed 
to be endowed with a spirit, or anima. 

Gradually, however, the distinction between animate and 
inanimate objects becomes clear. Accordingly, we find 
that at a somewhat more advanced stage the mode of explana- 
tion takes a different form, though it is still anthropomorphic. 
Physical objects are no longer regarded as having life in 
themselves; the changes in them are supposed to be due to 
the action of spirits, who are separate from the objects, but 



§ ^9' Jtidgmefits of Causal Connection 365 

who use them to accomplish their purposes. These invisible 
spiritual agents, to whom all natural events are referred, have 
been variously named. It is clear, however, that the gods 
of mythology belong here, as well as the fairies, elves, ghosts, 
and witches of the popular folk stories. It was a great ad- 
vance when a Greek thinker, named Thales, came to the 
conclusion that it does not in any way explain natural events 
to refer them to the action of the gods. For, in the first place, 
to say that the gods cause this or that event, is to state some- 
thing which we have no means of proving. And, even if the 
assertion were true, it would not really explain anything. 
For it would not enable us to understand how the changes in 
question came about. It would tell nothing whatever re- 
garding the actual steps in the process itself. Thales saw this, 
and tried to give a natural explanation of the world, and all 
that goes on in it. He tried to build up a real system of know- 
ledge by attempting to show how everything which has 
happened in the world has been connected with some natural 
cause. We know very little about the actual explanation of 
the world which Thales gave, except that he tried to derive 
everything from water. It is on account of the method which 
he adopted, rather than of what he actually performed, that he 
is regarded as the founder of science. Thales first showed, 
one may say, that knowledge means an insight into the ways 
in which the actual phenomena of the world are connected with 
one another. We cannot unite into a system things so differ- 
ent in kind as spirits and natural phenomena. Or we may 
say that real explanation demands that there shall be some 
likeness, or ground of similarity, between the cause and the 
effect. An event which happens in the world of objects 
must be explained by showing its connection with some 
other, event, of a similar character, on which it depends. 



366 Types of Judgment 

The development of this conception of scientific explanation 
also influenced still further the notion of causality. We have 
seen that in the beginnings of knowledge every event was 
supposed to be due to the action of some living agent, or 
spiritual being. Even after this mythological mode of expla- 
nation is discarded, and natural causes put in the place of 
spirits, it is still difficult to rid oneself entirely of the old 
anthropomorphism. The popular mind still tends to regard 
the cause as an agent which produces the effect, through 
some power or efficiency which it possesses. It is not neces- 
sary to raise the question "at present whether there are any 
grounds for this belief. To discuss this problem vv^ould carry 
us beyond logic into metaphysics. What we wish to notice is 
that science has gradually abandoned the notion that the 
cause does something to the effect. That, as we have seen, is a 
remnant of the old pre-scientific idea, and a notion which 
does not aid at all in explaining phenomena. It is the business 
of science to show how the things and events which make up 
our experiences are necessarily connected with one another. 
Science has to discover what things invariably go along with 
one another, and necessarily presuppose one another. And, 
when it is found that some particular thing or event. A, is 
invariably necessary for the appearance of another particular 
occurrence, B, the former is regarded a.s the cause, and the 
latter as the effect. In order to eliminate as far as possible 
the notion of agency or efficiency which attaches to the word 
cause, the terms ^ antecedent ' and ^ consequent ' are often used 
to indicate this relation. For science, the cause is not an 
active agent, but the invariable and necessary antecedent of 
something else which simply follows it. The cause does not 
explain the effect by assigning an agent which brings the 



§ 89- Judgments of Causal Connectio7t 367 

latter about through its personal efforts; but it explains, be- 
cause it reveals another necessary step in the process, and 
gives us a new fact which joins on or can be connected with 
the one from which we start. 

We conclude then that the cause of any event is its invari- 
able and necessary antecedent. It has been already explained, 
however, (p. 237) that by antecedent is not meant merely 
that which is prior to the effect in time. The word must 
be understood as signifying the essential condition or what is 
' logically ' prior. Temporal priority is often taken practically 
as an indication of logical priority, but the two relations can- 
not be identified. In another part of this book (Chs. XVI., 
XVII. ), it is shown what tests it is necessary to apply in 
order to determine whether two phenomena are merely 
accidentally conjoined, or whether the connection is essential 
and real. It is necessary now to take one more step in tracing 
the various ways in which the idea of causality has been used. 
As a result of a famous scientific discovery, which was made 
about the middle of the preceding century, a new element 
has been added to the notion of cause in its application to 
physical phenomena. The law of the Conservation of Energy 
states that the amount of energy, or power of doing work, 
possessed by any set of bodies, regarded as a closed mechani- 
cal system, remains constant. Any change in a material body 
is the result of a transformation of energy from one form to 
another. The same notion is applied to the world as a whole : 
it is assumed that the total amount of energy which it con- 
tains remains constant. All changes which take place in the 
physical universe — motion into heat, or electricity into mo- 
tion — are regarded as simply different forms, or manifesta- 
tions, of the one world-energy. 



368 Types of Judgment 

As a result of this law, the effect always represents the same 
amount of energy, or power of doing work, as the cause. 
Since no energy is ever lost, the one must be equal to the 
other. And, as a matter of fact, the quantitative equivalence 
of many of the various forms of energy has been proved by 
actual measurement. In working out this law, for example, 
Joule showed that ^^ the energy stored up in the i-lb. weight 
which had been pulled up 772 feet was gradually transformed, 
as soon as the weight was released, into an amount of heat 
capable of raising the temperature of a pound of water i ° Fahr. ; 
while Hirn showed, on the other hand, that exactly this 
amount of heat would, if it could be turned back again into 
energy, raise the i-lb. weight to the height of 772 feet at which 
it stood before.' ' ^ 

The new element which this law adds to the idea of cause as 
a necessary and invariable antecedent, is that of the quanti- 
tative identity of cause and effect. Taking the phenomena 
which are connected in this way to represent simply certain 
quantities of energy, we say that the one is equivalent to the 
other. The energy which the cause represents has been 
transformed without loss, and reappears in the effect. If 
what seems to be the total effect is not equal to the cause, part 
of the energy of the latter must have been transformed into 
something else as yet perhaps unnoticed. No energy can 
have been lost. 

It becomes, therefore, the task of the physical sciences to 
show that this relation of quantitative identity exists between 
phenomena which are causally connected when these are re- 
garded by the science as constituting a closed mechanical 
system. The ideal of physical science is to prove that two 
^ Buckley, Short History of Natural Science^ p. 339. 



§ 89- Judgments of Causal Connection 369 

groups of phenomena are connected as cause and effect, by 
showing that both represent the same quantity of energy. For 
this purpose, measurement and calculation are necessary. 
The physical sciences, as was pointed out in the last section, 
deal largely with judgments of quantity, and devote them- 
selves to showing by measurement that the same amount of 
energy persists through the various changes which phenomena 
undergo. In establishing causal connections, therefore, the 
physical sciences find it necessary to use the principles of 
measurement and calculation. 

It will be evident, from what has been already stated,. that this 
relation of cause and effect should, in theory, apply to all phenomena 
whose energy is capable of being measured and represented in 
quantitative terms. As a matter of fact, however, the law has been 
proved only in physics and chemistry. From the very nature of 
the case, it is extremely difficult to measure exactly the relations 
of cause and effect in the sciences which deal with organic life. 
But even in those sciences, the law of the Conservation of Energy 
is assumed to hold true. For example, the amount of energy 
v/hich a plant contains, is assumed to be exactly the same as that 
represented by the various elements or forces — water, sunlight, 
mineral substances, etc. — which were instrumental in composing 
it. In the same way, we suppose that the same relation holds of 
the changes which go on in the brain, though we are, of course, 
unable to prove this by actual measurement. We may accordingly 
speak of the law of the Conservation of Energy as the working 
postulate of these sciences. 

It is difficult, however, to see how this law can have any applica- 
tion to mental phenomena. We can indeed measure the intensity 
and duration of sensations. But neither feelings nor complex 
processes of mind seem to be capable of measurement in fixed and- 
unambiguous units. Moreover, it is never possible to measure 

2 B 



370 Types of Judgment 

the energy, or power of doing work, which states of consciousness 
possess, and to equate one with another in this respect. And this 
being so, the law of the Conservation of Energy cannot, of course, 
apply to psychical causes and effects. In the mental sciences, 
then, we cannot claim that the notion of Causality contains the 
element of quantitative identity between cause and effect which 
has been found to exist in the physical sciences.^ 

§ 90. Judgments of Individuality. — By Judgments of 
Individuality, we mean judgments which regard some 
complex object as a real whole with a definite nature of its 
own. Judgments of this kind are also frequently called 
Judgments of Purpose, or Teleology. We have already had 
occasion (§ 78) to distinguish a mere aggregate or sum of 
parts, like a heap of stones, from a true whole which pos- 
sesses a certain character and individuality of its own. It is 
as aggregates rather than as true wholes that judgments of 
quantity and of causal connection regard objects. For these 
types of judgments are concerned with the parts — the 
former to measure them, and the latter to show their causal 
connection. It requires a new form of judgment to represent 
adequately the nature of a complex object which possesses 
individuality. This form gives expression to the organic unity 
and v/holeness of things, and emphasizes the way in which 
the parts cooperate for a common purpose or end. Thus we 
regard the parts of a plant as a unity cooperating in a common 
purpose, and a man as a conscious system of ends. The 
question as to whether it is allowable to employ any other 
category, or form of explanation, in science than that of cau- 
sality, is of great importance. In biology, for example, 
it is usual to explain certain structures of plants and animals 

^ Cf. Wundt, Eihik (ist ed.), pp. 398 f.; Sigwart, Logic, § 97 a, 7. 



§ 90- Judgments of Individuality ^^i 

as purposive. How far, now, is it allowable to go in substitut- 
ing this teleological form of explanation for explanation in 
causal terms? This question is too large to be discussed 
here, but it is suggested as of fundamental importance both 
for science and philosophy. 

(i) We have seen that judgments of causal connection relate 
phenomena as causes and effects. A change in an object is ex- 
plained by showing that some other change or event invariably pre- 
cedes it. But this change, in its turn, demands explanation, and 
has to be accounted for by the discovery of a new cause. This 
type of judgment shows that one phenomenon is connected with 
a second, a second with a third, and so on indefinitely. The 
view of the world which it presents is that of a never-ending series 
of causes and effects. It is never possible to find a cause which is 
not itself the effect of something else. No phenomenon possesses 
any independence of its own, but is simply a link in a series, or a 
piece of a whole that is never completed. We say, therefore, that 
causal explanation leads to an infinite regress. The notion of a ^ first 
cause' is then contradictory, if 'cause' be defined in the scientific 
sense, as a phenomenon existing in time and space. 

In the last section, it was stated that causal judgments connect 
one part of our knowledge with another, and, in this way, aid in 
uniting the parts of our experience in a systematic way. Now it is 
undoubtedly true that it would be impossible to have any genuine 
knowledge of anything as a whole, or an individual, without know- 
ing the way in v/hich the parts are related, and mutually depend 
upon each other. In that sense, judgments of causal relation are 
indispensable to a knowledge of a true whole. But this form of 
judgment itself resolutely goes on connecting part with part — one 
phenomenon with another — and refuses to regard any group of 
parts as possessed of an independent character or individuahty. 
From this point of view, everything is externally determined; its 



372 Types of Judgment 

cause, or principle of explanation, lies outside of it in something 
else. The mark of individuality, on the other hand, is the power 
of origination, or self-determination. If, then, there exist any 
genuine individuals, they are something more than causally de- 
termined phenomena. 

(2) Psychology, at least modern structural psychology, adopts 
the standpoint of Causal Connection; while Ethics, assuming that 
men as moral beings are responsible for their actions takes to some 
extent at least the standpoint of Individuality. The former 
science regards mind as a sum of mental processes, and under- 
takes to show how its various parts are connected. Every state 
of consciousness is supposed to be determined by something external 
to itself — some antecedent mental state, or some bodily process. 
The interest, as was previously said, is centered in the parts, and it 
is very rarely that the psychologist stops to look at the mind as a 
whole. Ethics, on the other hand, has to begin with the individual. 
It does not regard mind as a thing or substance (that is the naive 
point of view against which psychology rightly warns us), but as 
a self-conscious system of ideas, purposes, and feelings, which pos- 
sesses the power of initiating action, and of determining itself in ac- 
cordance with some purpose. The judgment of Individuality, 
as a more concrete form, must use the results of judgments of 
Causal Connection. What it really does, is to interpret what for 
the psychologist is a sum of mental processes in terms of a 
system which has a real unity of its own. For it is only when a 
person is regarded as a self-conscious and self-acting individual, 
that he can be supposed capable of conduct to which the terms 
'morar and 'immoral' can properly be applied. 

REFERENCES 

Hegel, Logic, Pt. II., The Doctrine of Essence (Wallace's trans. 2d 
ed.), pp. 206-286. 

B. Bosanquet, Logic, Vol. I., Chs. II.-V. 
J. S. Mill, Logic, Bk. IIP, Ch. V. 

C. Sigwart, Logic, § 73. 



CHAPTER XXV 

THE NATURE OF INFERENCE. — INDUCTION AND DEDUCTION 

§ 91. Judgment and Inference. —It must not be forgotten 
that our object in these chapters is to obtain as definite a con- 
ception as possible regarding the nature of thought. To 
attain this end, we agreed (§ 73) that it would be advanta- 
geous to begin with the simplest or most elementary form of 
thinking. That form we found to be Judgment. We have 
now endeavoured to show what Judgment is, and what part 
it plays in building up knowledge. And, in the last chap- 
ter, we have attempted to see some of the steps in the evolu- 
tion of Judgment, as it passes from simple judgments of 
Quality to judgments of Individuality. This account being 
completed, it remains now to discuss the nature of Reasoning, 
or Inference, as the process in which judgment occurs. 

We shall probably get the clearest idea of the nature of 
Inference by regarding it as a com^pletely developed judg- 
ment. As thinking develops from the form of simple judg- 
ment to that of Inference, it displays progressive differen- 
tiation and integration. In accordance with this law, we 
can say, (i) that Inference is more complex than Judgment. 
The latter process, in its sim_plest form, can scarcely be said 
to have any parts: it represents a single act or pulsation of 
intelligence. Inference, on the other hand, seems to imply 
steps or stages in thinking — a passage of the mind from one 

373 



374 '^^^ Nature of hiference 

fact to another. Moreover, (2) Inference differs from Judg- 
ment in exhibiting the grounds upon which its statement 
rests. The simple judgment makes a declaration on the basis 
of sense-perception, as, for example, ^ the mail-train has just 
gone down'; ^ it rained yesterday.' Each of these state- 
ments stands alone, as it were; it does not attempt to gain 
support by pointing out the connection of the asserted fact 
with other facts. To infer, however, is just to show the nec- 
essary connection of facts — that from the presence or ab- 
sence of certain things, the presence or absence of certain 
other things necessarily follows. It is not necessary for 
Inference that the conclusion reached should be a fact which 
was not hitherto known. We often do reach new truths by 
reasoning from necessary connections. Thus we might 
infer that the mail-train has just gone down, from the fact 
that this train is always on time, and that it is now five min- 
utes past the hour. Or, we might prove, to a person who 
doubted the correctness of our memory, that it rained yester- 
day, by pointing to other facts with which rain is necessarily 
connected. We might point to the mmddy condition of 
the roads, the swollen streams, or, perhaps, might remind 
the person who questions the statement, that it was yester- 
day that A was out driving, and came home soaking. In 
this way, one tries to exhibit the necessity of the fact under 
consideration; and to do this is to infer. 

But in the actual process of knowledge, we more frequently 
go from a fact to its reasons, than in the opposite direction. 
The intelligence begins by accepting all the connections as 
true and universal which it meets with in ordinary expe- 
rience, or which are suggested to it in any way. It does not 
trouble itself at all about the grounds of its judgments, and 



§ 91- Jttdgment mid Inference 375 

thus the insufficient basis on which many of these stand is at 
first not evident. The child, for example, believes every- 
thing which it is told by its mother or nurse, or, it may be, all 
the pleasant things which it imagines. Very often, too, the 
judgments of older persons are determined by their own 
wishes. The French peasant girl was sure that it was im- 
possible for the Germans to take Paris. Another principle 
upon which both children and adults quite unconsciously 
proceed, is that the future must always resemble the past. 
The child assumes that the order of events each day will be 
the same, — that there will always be games after dinner, 
and visitors in the afternoon, because that has happened a 
number of times in the past. And one may have no better 
reason for believing that the sun will rise to-morrow, than 
the fact that it rose yesterday and to-day. 

In these early, unreflective judgments, the ground or prin- 
ciple upon which they are based is, of course, not conscious 
at all. Each judgment is accepted by itself, and no questions 
are raised as to how it is known. But the development of 
intelligence may be regarded as a process of becoming con- 
scious of the reasons which show the falsity of certain of our 
beliefs and the necessity of others. The original judgment 
is not in reality so isolated and unrelated as it appeared; it 
contains implicitly its own reasons. But the validity of 
its procedure cannot be made manifest, until the reasons 
for the statement made by the judgment are brought to light. 
In the development of knowledge, the judgment must ex- 
pand so as to show the reasons which it necessarily presup- 
poses. In itself, it is only a fragment of the complete state- 
ment, and it tries to complete itself by making clear the nature 
of the whole which it involves, or to which it really belongs. 



376 The Nature of Inference 

It is not until the implicit reasons which every judgment 
contains are thus brought to consciousness^ that it can be 
either proved or disproved. Taking the mere judgment 
by itself, it is only possible to place one man's assertion 
against another's denial. But proof or disproof of a propo- 
sition implies that reasons are given for or against it. If its 
connection with some fact, or set of facts, known to be true, 
becomes evident on reflection, the felt necessity v/hich the 
judgment possesses (§ 8i) is transformed into a logical 
necessity. But, if no such connection can be found, or, if 
the judgment in question is seen to presuppose propositions 
which are themselves false, we must, of course, cease to 
regard it as valid. 

/ When a judgment develops so as to become conscious of 
/ its reasons, it has already taken on the form of Inference. 
And, as we have already seen, this is the usual procedure of 
knowledge. We begin by believing without reason, or we 
assume that certain things are true, and try to find reasons 
for our belief. The conclusion, which is, of course, logically 

, last, is usually first for us, and we set out from it to find the 

^ grounds, or the premises. 

This way, however, of proceeding from conclusion to prem- 
ises, or from a judgment to its reasons, im_plies that the 
mind is already aware of the distinction between false know- 
ledge and true, and therefore that the work of criticising and 
testing knowledge has already begun. The criticism of knowl- 
edge is probably forced upon the mind at first by the practical 
consequences of false judgments. So long as false judgments 
lead to no unpleasant results, they are likely to pass unnoticed, 
without any question being raised regarding the grounds 
by means of which they are supported. The child usually 



§ 91- Judgment and Inference 377 

believes all that he is told, until he discovers that his credu- 
lity is making him a laughing stock, or has led to the loss of 
some pleasure which he values. Sooner or later he learns 
that the ground upon which he has been unconsciously pro- 
ceeding — somebody told me — is insufficient. In the same 
vv ay, the natural tendency to regard all connections which we 
happen to find existing between events as universal and 
necessary, becomes more critical and discriminating. The 
child soon learns that the events of one day do not necessarily 
follow in the order of the day before, and that it is not always 
rainy on Fridays, and fine on Sundays. But, in order to 
discriminate between what is true and what is false, he is 
obliged to go beyond the facts themselves, and to become 
more or less clearly aware of the grounds assumed in each 
type of judgment. He is forced to include in the judgment 
the reasons by which it is supported. And, in this way, the 
distinction between valid and invalid* principles of connection 
is gradually learned. Through experience, which is more 
or less dearly bought, we learn that we cannot depend 
upon hearsay, and also that many of the most obvious con- 
nections between events are not essential, and have no claim 
to be regarded as universal laws. It becomes evident that 
it is necessary, in order to reach true principles of connec- 
tion, to take a wider survey of the facts, and to push the 
process of analysis further than is done by our ordinary 
judgments of sense-perception. For example, we may at 
one time have supposed it to be a universal law that hot 
water will break glasses when poured into them. But as 
soon as we have experience of any instance or instances to 
the contrary, we see that there is no essential connection 
between hot water and broken glasses. It is necessary then 



3/8 The Nature of Inference 

to go behind the obvious facts of the case, in order to discover 
what is the real antecedent in the two cases. The two in- 
stances — where the glasses break, and where they do not — ■ 
seem to be the same ; and yet, since the result is different, 
there must be a difference which further analysis will bring 
to light, such as the greater thickness of the glasses which 
break. It is by penetrating beneath the point of view of 
ordinary knowledge, that science endeavours to show how 
phenomena are really and essentially connected. 

I The judgments of ordinary adult life usually involve some con- 
! sciousness of their grounds, and are therefore so far inferences. 
But in many cases of this kind it would be difficult for the individual 
to state explicitly the reasons for his judgment. The connection 
which he asserts may be guaranteed to his mind by some complex 
set of circumstances very difficult to formulate. Or it may rest 
upon some general similarity or analogy, which is so obviously in- 
sufficient that he hesitates to acknowledge that it is the only ground 
he has for judging. Thus one may be vaguely conscious that 
one's only reason for 1 king A is his resemblance to B. It may be 
impossible to say exactly in what points A resembles B ; one may 
proceed on a vague general similarity. Or one may hesitate to 
make clear, even to oneself, that the only reason for disliking A is 
because of some external resemblance — in name, or dress, or 
figure — to C, whom one dislikes. 

§ 92. The Nature of Inference. — We have seen that it is 
difficult to draw any hard and fast line between Judgment 
and Inference. In general, however, we may be said to 
reason when we do not simply accept a fact on the basis of 
sense-perception or memory, but show that it necessarily 
follows from some other known fact or facts. Inference, 
then, requires (i) that certain data or premises should be 



§ 92. The Nature of Inference 379 

accepted as already known; and (2) it implies an insight 
into the necessary connection of some new fact or set of facts 
with what we already know. Thus one is said to infer B 
when one sees that it necessarily follows from some fact 
which is already known. It is not necessary for an inference 
that B should never have been in consciousness before. As 
we have seen in the last section, what we very often do in 
inference is to show the reasons or necessity of some fact 
which we have previously accepted without knowing v/hy. 
No matter whether we go from premises to conclusion (from 
the reasons to the fact) , or in the opposite direction, from the 
conclusion to the premises, we are said to infer whenever 
we find the ground for the existence of one fact in the nature 
of another fact. In the former case, we use words like ^ there- 
fore ' and ^ consequently,' to indicate the connection; or, 
when the reasons are stated last, we use ^ for ' and ^ because.' 
Whenever these conjunctions are used correctly, an inference 
has been made, and it is always useful in following a course 
of reasoning to make clear to ourselves precisely on what 
groimds it has been made. 

Although Inference seems very simple and very natural, 
its procedure is much more puzzling, when looked at closely, 
than one would at first imagine. As we have seen, there is 
no Inference unless the result reached is different from the 
starting-point. But how are we ever justified in passing from 
a knowledge of one fact to another different from it ? How 
can we ever pass from the known to the unknown ? The 
Greeks, who loved to bring to light the paradoxes which so 
often underlie familiar facts, used to discuss this question. 
How is it possible for that which is unknown — external to 
the mind — to pass into the mind and get itself known? It 



380 The Nature of Inference 

was to solve this puzzle that Plato propounded the doctrine 
that all knowing is remembering.^ Knowledge, he declared, 
is not increased by learning that of which we were altogether ; 
ignorant, but by a process of calling to mind or recollecting | 
the knowledge which the soul possessed in a previous state 1 
of existence, but which was forgotten when it entered upon , 
the conditions of the present life. It was therefore not neces- 
sary to suppose, according to Plato, that the. mind performed 
the impossible feat of knowing what is external to itself, or 
that things previously unknown pass bodily into our minds, 
and thus become known. 

Plato was undoubtedly right in protesting against the 
popular view that knowledge is received into the mind in 
mechanical fashion, as food is received into the stomach. 
Knowledge, as we have frequently seen, is built up from 
within, and not put in from without. But the apparent para- 
dox of knowledge may be explained without adopting Plato's 
poetical notion of a previous state of existence. We may 
admit that the process of inference would be quite inexpli- 
cable, if it proceded from one fact. A, to a knowledge of a sec- 
ond fact, B, which is totally different from the former. When 
we examine cases of inference, however, we find that there is ., 
always a certain amount of identity between the two ends of 
the process. The conclusion is always different, and yet not 
entirely different from the premises. Thus, from the propo- 
sitions, ' all metals are elementary substances,' and ^ gold is 
a metal,' one can infer that gold is an elementary substance. 
It is possible to connect ^ gold ' and ' elementary.' Here the 
identical link — what is called in formal logic the middle 

^ This is the theory upon which Wordsworth based his *' Ode on the 
Intimations of Immortahty." 



§ 92. The Nature of Inference 381 

term — is ^ metal.' It is possible to connect gold and ele- 
mentary substance, because the former is at the same time a 
metal, which in its turn is an element. Of course, these con- 
ceptions — gold, metal, element — are not absolutely iden- 
tical ; it was pointed out in § 84 that propositions cannot 
be regarded as expressing mere identity without difference. 
But we can say that there is a common thread or element 
running through these notions, which furnishes the principle 
of connection. Where we cannot discover such a common 
nature, no inference can be made. Thus, for example, it 
would be impossible to draw any conclusion from the state- 
ments that ' it rained yesterday ' and ' gold has been dis- 
covered in Alaska,' because there is no common element or 
connecting thread present which would lead us beyond the 
premises. 

In formal arguments the middle term, or connecting link, 
is usually explicitly stated; but in the actual process of rea- 
soning things out, it is frequently necessary to go in search 
of it. We may notice, for example, that the fire in a stove 
burns more slowly when the damper is shut. In order to 
understand the fact, v/e have to find out some fact which is 
common to ' closed-damper ' and ' slow-burning,' some link 
of identity, as it were, which enables us to pass from the one 
to the other. Such a connecting link is afforded, of course, in 
this case by the supply of oxygen. Darwin was noted for his 
keenness in detecting connections which escape the ordinary 
eye, as well as for his skill in giving explanations of them. 
On one occasion, he observed that in the part of the country 
where he lived, clover was abundant in those fields which 
were situated near villages, while the outlying fields were 
almost destitute of it. What now, he asked himself, is the 



382 The Nature of Inference 

connecting link between these facts ? Some investigation 
of the matter convinced him that the three agencies which 
produced this result were humble-bees, mice, and cats. The 
bees fertilize the clover flowers, and thus make the plant 
abundant, the field mice destroy the bees' nests, but the cats 
go out from the villages into the fields near by and kill the 
mice. 

We have seen that the passage from one fact to another in 
inference does not involve a transition to something wholly 
different from the starting-point. There is always some 
aspect or feature in which the premises are identical with 
the conclusion. And it is on the strength of this identity 
that a passage can be made from one to the other. The same 
fact may be expressed differently by saying that all inference 
takes place within a system, ^ where the parts are so held 
together by a common nature that you can judge from 
some of them what the nature of the others must be.' Sup- 
pose you were given the leaf of a plant. If you had some 
systematic botanical knowledge, it might be possible to infer 
the species of plant to which the leaf belonged. That is, 
from the nature of a part, the nature of the whole to which 
it belongs could be determined. The part represents the 
whole — in some sense contains it implicitly. It is said 
that the great naturalist Cuvier could determine by exam- 
ining a single tooth the nature of the animal to which it 
belonged. Let us suppose that the tooth were that of a 
ruminant animal. Now a zoologist, who knows the character- 
istics of such an animal, could draw various inferences regard- 
ing the possessor of the tooth. He could conclude, for 
example, that the animal to which it once belonged must also 
have had cloven hoofs. A single piece or part, that is, would 



§ 92. The Naticre of Inference 383 

enable one who knows accurately the system or common 
nature to which all the parts belong, to judge what the other 
parts are like. 

The examples just given have referred to the possibility 
of an inference from one part of an organism to another. But^ 
as we have already seen, the systematic connection which 
here exists between the parts is more or less completely 
present whenever it is possible to infer at all. Inference 
pushes further the work of constructing a system begun by 
Judgment (§ 83). If each thing were known by itself, if the 
parts of our knowledge did not fall together into systems 
where each part to some extent determines the nature of the 
other parts, no inference would be possible. It is because 
the various pieces of our knowledge are never independent of 
one another, but form an organic whole, like the members of 
a living organism, that certain facts follow, as we say, from 
certain other facts. Otherwise we could only guess, or infer 
vaguely on the expectation that the future will resemble the 
past. Even this expectation, however, has no rational 
basis, unless the world does form some kind of a coherent 
system. It is, of course, true that practically a great deal 
of the knowledge of every one is unsystematic, being com- 
posed of facts and theories which have never been brought 
into relation. But knowledge is not to be described in terms 
of such defects in the case of individuals. To understand it, 
we must take it at its best and in its most complete form. It 
is obvious that, as our knowledge in any field becomes more 
completely and exactly organized, it it will be increasingly pos- 
sible to use it as a basis for inference. The better we are able 
to put together in a systematic way the various facts which 
we have learned about geology, or astronomy, or the weather, 



384 The Nature of Inference 

the more significant each fact becomes. The geologist may 
be able to tell from the appearance of the cliffs what has 
taken place in a locality thousands of years ago. And^ 
similarly, for the fisherman, the temperature, direction of 
the wind, its rising or falling, etc., are all signs from which he 
is able to infer, more or less correctly, the kind of weather 
which may be expected. A person vv^ho had no systematic 
knowledge in either of these fields would, however, see noth- 
ing in the scarred rocks, or in the sudden changes of the wind; 
he might notice the facts, but would not be able to use them 
as a basis of inference. 

It is important to notice that what has just been said goes 
to confirm our previous statements regarding the increasing 
degree of integration which knowledge shows in the course 
of its development. The knowledge of the scientist differs 
fromx that of the ordinary man, not only in the greater number 
of facts which the former contains, but also, as we have seen, 
in the degree of integration or coherence which these facts 
possess. Inference, then, is simply a deep insight, based on 
definite knowledge, into the necessary connection of things. 
It is an act of thought which discovers the essential relations 
between things which at first sight appear to have no con- 
nection with one another. As has already been said, it is a 
reasoned judgment; i.e. a judgment which has become con- 
scious of the reasons for the connections which it affirms. 

§ 93. Induction and Deduction. — It has been already 
pointed out that there are two directions in which inference 
or reasoning may proceed. We may begin with certain 
facts or principles which are already known, or are assumed 
to be true, and proceed to show that some result necessarily 
follows from them. Thus we might infer, from our know- 



§ 93- Induction and Deduction 385 

ledge of chemical principles, that if the draughts of a stove are 
closed so that the supply of oxygen is lessened, the fire will 
burn slowly; or from the relative positions and revolutions 
of the planets, astronomical reasoning might lead to the con- 
clusion that an eclipse of the sun will take place on a specified 
day and hour. This method of reasoning is known as De- 
duction. It proceeds, as we have seen, from premises to 
conclusion. In the first part of this book, this form of reason- 
ing has been treated at some length and its rules of procedure 
stated. At present, we need only notice that in deductive 
reasoning, the particular case is always brought under some 
general law or principle, which is already known or assumed 
as true. Socrates is known to be mortal, because as a man he 
falls under the general law that all men are mortal ; the clos- 
ing of the draughts is a case of lessened supply of oxygen, 
and, therefore, in accordance with the general law, a case of 
slow burning. A deductive inference shows what are the 
results of the application of a general law to particular facts 
or instances. It proceeds downwards, as it were, from the 
general law to its consequences. 

In Induction, on the contrary, the procedure is just the 
opposite of this. We begin with particular phenomena, and 
try to discover from them the law or principle which unites 
them. Certain facts are observed to happen together, and 
the problem is to find the ground or explanation of this con- 
nection. Inductive inference is thus a process of reading 
the general law out of the particular facts, of transforming 
the hypothetical answer to the problem into a systematic prin- 
ciple or theory. It is an insight into the nature of the whole 
or system, based upon a careful examination of the parts. 
* Yesterday the smoke tended to fall to the ground, and it 

2C 



386 The Nature of Inference 

rained in the afternoon.' These two facts may simply be 
observed a number of times without any thought of their 
connection. But intelh'gence asks: Why should they happen 
in conjunction ? And to answer this question, we must 
begin by analyzing the facts in our possession. When the 
smoke falls to the ground, the atmosphere must be lighter 
than usual ; this is the case when it contains a great deal of 
moisture; but when the atmosphere is in this condition, it 
usually tends to discharge its moisture in the form of rain: 
therefore we have the general law which enables us to show 
that the behaviour of the smoke and the rain yesterday were 
not only accidentally conjoinedj but essentially connected. 

Deduction and Induction, then, are both forms of infer- 
ence, but the starting-point and mode of procedure of the 
one is different from that of the other. Consequently, it is 
not unusual to speak of them as two kinds of reasoning which 
are quite distinct and independent of each other. It is, how- 
ever, important to avoid this popular error, and to remember 
that the real process of inference is in each case the same. 
The essence of inference, as has been shown, consists in the 
fact that it exhibits the manner in which particular facts are 
connected together into a system or whole. And this end is 
achieved by both Deduction and Induction. In the former 
case, the general law of connection — what we may call the 
nature of the system within which the particulars fall — is 
known, and we argue from this as to the nature and relations 
of the various parts which fall within it. We have the com- 
mon thread which unites the various facts in our hand, and 
following it out are able to show its application in determining 
the nature of events which have not yet come within the range 
of our experience. Knowing the law of gravity, for example, 



§ 93- Induction and Deduction 387 

one could infer deductively what momentum a ball weighing 
one pound must necessarily have after falling one hundred 
feet. It would not be necessary actually to measure the mo- 
mentum of the falling body in this particular case, but it 
could be shown to be the necessary result of the general law. 
What the deductive inference shows us is the way in which 
a general principle or law of connection runs through a group 
of facts, and constitutes them a real or organic whole. The 
same insight is reached by inductive inference, although the 
starting-point is entirely different. As we have already 
seen, induction begins by observing that certain phenomena 
are frequently conjoined, and attempts to discover some law 
or principle which will make the fact of their connection 
intelligible. 

It is usual to say that in induction we go from the par- 
ticular facts to the general law. The following, however, 
would be a more correct form of statement: Before the 
inference, we observe that a number of phenomena occur 
together, but do not know whether this conjunction is nec- 
essary or not ; or, if we assume that it is necessary, we do 
not understand why it should be so. As a result of the induc- 
tive inference, we gain an insight into the necessary connec- 
tion of the observed phenomena, and also understand the 
principle according to which the latter are united. What 
we really obtain through an inductive inference is not only a 
general law, but also a perception of its concrete application 
to particular phenomena. This being so, it is clear that 
Induction and Deduction are not two different kinds of 
inference. Inference always implies an effort on the part 
of the mind to see how phenomena are necessarily connected 
according to some general principle. And, in carrying out 



388 The Natm^e of Inference 

this purpose, the mind must begin with the knowledge which 
it already possesses. When the general law of connection 
is known, and the object is to discover the nature of some 
particular fact, the method of procedure is deductive. But, 
when the problem by which we are confronted is to read out 
of the facts of sense-perception the general law of their 
connection, the method of inference which must be employed 
is that of Induction. But, from whatever point we set out, 
and whatever may be the immediate object of the inference, 
the result is always the same — an insight into the necessary! 
connection of facts according to some general principle. 

It is not unusual to hear the remark made that modern 
science has been built up by the employment of the inductive 
method. This must not, however, be interpreted to mean 
that deductive inferences are not also used in the discovery 
of scientific truth. Science (which is simply another name for 
systematic knowledge) is the product of thinking ; and thought, 
as we have seen, is not limited to any one mode of procedure. 
Thought aims at extending knowledge, and so long as it can 
find any link of connection, or guiding thread, it is not limited 
to any one direction, or to any fixed mode of working. It is, 
of course, to be admitted — and this is true in the statement 
which we have quoted — that general laws cannot be dis- 
covered without an examination of particular facts, and that 
their validity must always be tested by comparison with the 
facts. But as soon as a general law is discovered in any 
field, it is always used as a principle from which to deduce 
new results. When it is possible to employ mathematics in 
the calculation of these results, it is usually possible to extend 
our knowledge of the subject much more rapidly than before. 
Thus physics and astronomy owe their rapid development to 



§ 93- Induction and Deduction 389 

the application of mathematics. It must be remembered, 
however, that this presupposes a certain stage of advance- 
ment — a certain inductive stage, as it were — on the part of 
the science. But even in this earher stage we are constantly 
employing deduction, alv/ays reasoning out the results of cer- 
tain guesses or suggestions to see if they hold true (cf. § 48). 
Both in ordinary life and in scientific procedure Induction 
and Deduction are constantly employed together as mutually 
supplementing each other in the work of organizing expe- 
rience. 

REFERENCES 

B. Bosanquet, Logic ^ Vol. II., Ch. I. 

F. H. Bradley, The Principles of Logic ^ pp. 430-468. 

W. James, The Principles of Psychology^ Vol. II., Ch. XXII. 

J. G. Hibben, Inductive Logic, Chs. I. and II. 



CHAPTER XXVI 

THE UNIFICATION OF KNOWLEDGE 

§ 94. Science and Philosophy. — Throughout the pre- 
ceding chapters thinking has been described as the function 
through which the organization of experience is achieved, 
or as a process of building up a system of knowledge. It 
has become clear that the development of thinking involves 
a continuous increase in both differentiation and integration, 
and that these two moments or aspects of thought are or- 
ganically related to each other. An advance in knowledge 
implies at once new facts and distinctions, and also the per- 
ception of new connections and relations among facts. The 
ideal of completed knowledge, accordingly, would be a 
system of truths in which the place and meaning of every 
fact would be completely defined, and where, at the same 
time, the complete relation of every fact and every group of 
facts to every other would be fully exhibited. Nothing 
would then be indefinite for knowledge, and nothing would 
be isolated; to know things in this completely systematic 
way would be to see the world steadily and to see it whole. 

Like all ideals, this conception is never completely realized 
in experience as we know it. This, however, does not 
render it idle or without practical significance. In the first 
place, it has importance as indicating the direction in which 
the further development of knowledge must proceed. And, 
secondly, it is only by reading our actual knowledge in the 

390 



§ 94- Science and Philosophy 391 

light of the end towards which it is progressing that we are 
able to understand its nature. That is, as stated in the 
first section of this book, thinking has to be defined as the 
function, or system of functions, whose end and goal is know- 
ledge. Now knowledge is only attained in so far as unifica- 
tion and system are attained: the essence of knowledge is 
not found in its lack of system and definiteness — these 
are its defects and privations — but the cognitive experience 
of any individual has a right to the title of knowledge 
just in so far as these conditions are realized. 

The problem of how a more complete unity of knowledge 
than that realized in the results of the special sciences is to 
be attained, thus becomes of the highest importance. We 
may use the term Science to denote the entire work of dis- 
covery and systematization of facts which is carried on by 
the various civilized nations through successive generations 
and centuries. In this inclusive sense, Science is undoubt- 
edly one of the greatest achievements of the human race, 
and one of the highest objects of endeavour for the individual. 
Within this one body of knowledge, however, it is possible 
to make various distinctions between different sciences and 
groups of sciences. The various sciences might be clas- 
sified, for example, as more or less abstract, or as more or 
less inclusive in character. Or again, the sciences of nature 
might be distinguished from the humanistic sciences, which 
deal with the distinctive products of man's life and thought, 
as shown, for example, in religious, social, or political 
institutions, or in art, science, and philosophy. But the 
division of the complete body of knowledge (Science, 
Wissenschafi) with which we are here directly concerned, 
is that between the sciences and philosophy. For philos- 



392 The Unification of Knowledge 

opliy is the name given to the endeavour to reach some 
rational unification of the knowledge derived from the 
various forms of experience, and especially from the various 
sciences. ^'Knowledge of the lowest kind/' said Herbert 
Spencer, ''is un-unified knowledge; science is partially- 
unified knowledge; philosophy is completely-unified know- 
ledge.''^ We may accept this statement with the under- 
standing that of course no knowledge is entirely un-unified, 
and that, on the other hand, no actually existing system of 
philosophy can claim to have achieved a complete and satis- 
factory unification of knowledge. 

At the present time the systematic interpretation of the 
nature of the real world has been divided into various fields of 
investigation. Each science takes as its subject-matter a 
definite field, or group, of phenomena and endeavours to 
describe and explain, as accurately as possible, the facts that 
fall within that field. Thus, for example, astronomy studies 
the heavenly bodies with the purpose of making clear and 
comprehensible their changing phases and relations ; botany 
deals with the various forms and functions of plant life; 
history describes the significant events which have occurred 
during the past life of man in society. It is, however, not 
true that the sciences can be distinguished merely with refer- 
ence to the nature of the particular field which they occupy. 
The same body of facts may be dealt with by a number of 
sciences ; or, rather, there are certain more general or funda- 
mental sciences whose principles and results have to be 
employed in the work of the more special fields of inquiry. 
In botany, for example, physical and chemical facts and 
laws are cited in order to render the behaviour of the plant 

^ First Principles J § 37. 



§ 94- Science and Philosopliy 393 

intelligible. In political economy, in like manner, one has 
to make constant use of history in the investigations which 
one undertakes. Nevertheless, even where two or more 
sciences seem to occupy the same field, it will be found that 
each has its own special way of reading the facts, so that 
strictly speaking, the same phenomena are never studied in 
the same way or with the same purpose in view. 

The question to be considered here, however, is the ques- 
tion of the relation of the special sciences to philosophy. 
It might appear at first sight as if the whole field of reality 
were occupied — or soon to be occupied — by the various 
sciences and that no problem were therefore left for phi- 
losophy. But the very fact that each science is obliged, in 
order to render its investigations definite and fruitful, to 
limit the field of its inquiry, makes necessary some attempt 
to bring the results derived from the different fields into 
relation. And, as will appear more clearly in the last section 
of this chapter, to correlate the results of these different 
scientific inquiries, which are gathered with various purposes, 
and often by the employment of quite different hypotheses, 
is not merely to set them side by side. The work that phi- 
losophy is called upon to undertake is to interpret these 
results in such a way as to render them coherent and think- 
able. Philosophy aims at unifying knowledge by finding a 
conception or set of conceptions which will enable us to 
think the world as some kind of a consistent system. It 
seeks to satisfy our demand for a world-view, a Weltan- 
schauung. When we take the widest and most accurate 
survey within our power of the facts of experience, what 
conclusions are we warranted in drawing regarding the 
whole system of things of which we are a part ? 



394 ^^^ Unification of Knoivledge 

In attempting to find an answer to this most practical 
question, it is of course necessary to take account of every 
well-authenticated form of experience, and to give to each 
its proper place and value. It is obvious, too, that the prob- 
lem is the final problem of knowledge, and one that cannot be 
finally and fully solved by any individual or by any generation. 
But that is not a reason for abandoning it as insoluble. In 
the first place, it is a problem to which human reason from 
its very nature can never be permanently indifferent. It 
is only the animals, Hegel remarks, who are not metaphy- 
sicians. It is true that the majority of men never apply 
themselves directly to the solution of ultimate philosophical 
questions; but every one holds, more or less consciously, 
and in more or less definite form, some conception regarding 
the nature of the world and his own place in it. It is per- 
haps most frequently from theology or from literature that 
men derive their world-view, and they hold this, not as a 
reasoned system of knowledge, but rather through belief 
in authority, or on emotional or aesthetic grounds. As 
distinguished from constructions of this character, philosophy 
aims at a reasoned system. Like the sciences, it discards 
both emotion and tradition as guides, and proceeding by 
means of careful analysis and definition, it subjects all 
hypotheses to rational criticism. Its postulate is that there 
is nothing irrational, or from its very nature incomprehen- 
sible, in the nature of the world. It is true that science 
and philosophy will never complete the work they are carry- 
ing on : the results arrived at are never final, but only start- 
ing-points for new investigations. But in the one case as in 
the other, the road is never barred; progress is always pos- 
sible if the problem is formulated in an intelligible way. 



§ 95* Science as Philosophy 395 

Two considerations, which are frequently overlooked, fol- 
low from the conception of philosophy as a construction that 
is being continuously achieved by the human race in the 
course of its history. The first is, that it would be idle for 
any individual to begin the work anew on his own account, 
refusing to learn or to profit by the labours of the past. And 
secondly, it is obvious that from the nature of the case 
there will be, as long as the human race endures, no ultimate 
or finally complete system of philosophy. When it is remem- 
bered that philosophy is the completion of the sciences, 
that the philosophical problem is the final problem of know- 
ledge, the fact that neither the foundations nor its outlines 
are yet finally determined will not appear either strange or 
discouraging. 

§ 95. Science as Philosophy. — In this connection, the 
question arises whether the conceptions employed by the 
sciences are not themselves capable of effecting a final 
unification of knowledge. Why is it necessary to turn to 
philosophy, or if the name of philosophy is still used to denote 
the most comprehensive science, why should not the ulti- 
mate account of reality be given in the same terms as 
the descriptions of the special sciences ? Why, in short, 
not accept as philosophy the general standpoint and results 
of the sciences ? 

As a matter of fact, this is often done. During the last 
two centuries — and more particularly during the last cen- 
tury — the greatest advances in knowledge have been 
attained in the field of the natural sciences. As a conse- 
quence, it has been natural to assume that the same suc- 
cess may be attained everywhere by employing the same 
unifying conceptions in the solution of all kinds of problems. 



396 The Unification of Knowledge 

Now the fundamental categories with which natural science 
operates are those of Quantity and Causality. The latter 
conception, when used exactly or scientifically, includes the 
former, as has appeared in our study of Induction (cf. 
pp. 255 ff.). The* assumption on which the causal category 
proceeds is that reality is composed of phenomena which are 
external to one another and at the same time dependent on 
one another. Every phenomenon is at once a cause and an 
effect. There obtains everywhere unvarying laws of connec- 
tion between all events so that nothing can be thought of as 
happening except in one determinate and fixed way. For 
every phenomenon a cause must be sought in some other 
phenomenon, or group of phenomena, and thus everything 
is determined or conditioned, both as to its existence and 
nature, by something external to itself. External determina- 
tion, or conditioning through something external to that 
which is to be explained, is thus the form of relation employed 
by natural science in its work of unifying knowledge. 

Now in attempting to interpret the entire world as a 
series of phenomena which are everywhere related in terms 
of cause and effect, one might be either more or less thorough- 
going and consistent. On the one hand, one might assume 
that the complete unification of knowledge demands that 
there shall be only a single series of causes and effects. This 
would imply that all the phenomena of which the world is 
composed are at bottom reducible to the same terms, and 
are all manifestations of some one material, or one prin- 
ciple. Or, on the other hand, it might be assumed that there 
is more than one series and more than one fundamental 
principle involved in the nature of things. The first view 
would be Monistic and the second Pluralistic. I have said 



§ 95- Science as Philosophy 397 

that the first is more thorough-going, because Pluralism still 
has to face the problem as to the relation of the different 
forms of existence which it assumes. What is it that unites 
the plural forms of existence into a single world, a 
universe ? 

Without entering into the arguments in support of either 
Monism or Pluralism, however, we may illustrate the appli- 
cation of the causal point of view when employed under either 
assumption. Let us first assume that everything in the 
universe, without exception, can be reduced to some physical 
principle. It is indifferent for our illustration whether 
that elementary term be regarded as matter or energy, so 
long as it can be measured and its exact results calculated. 
The place of philosophy and of all the sciences would then 
be filled by a universal system of physics which would be 
able to describe and explain all forms of existence and all 
changes in terms of its own principle. Not only that, but 
since it would deal with a strictly determined and calculable 
series of events, it would, theoretically at least, be able to 
predict all occurrences -of the future, both mental and physi- 
cal alike, down to the smallest detail. More than a century 
ago Laplace wrote: ^'We ought then to regard the present 
state of the universe as the effect of its antecedent state, 
and as the cause of the state that is to follow. An intelli- 
gence who for a single instant should be acquainted with 
all the forces by which nature is animated, and with the 
several positions of the beings composing it, if further his 
intellect were vast enough to submit these data to analysis, 
would be able to include in one and the same formula the 
movements of the largest bodies in the universe, and those 
of the lightest atom. Nothing would be uncertain for him: 



39^ The Unification of Knozvledge 

the future as well as the past would be present to his eyes.'' 
If now, as we are assuming, all phenomena are in the last 
resort reducible to some physical principle, Laplace's hy- 
pothetical calculator would also be omniscient with respect to 
all the contents of every mind that ever existed or will exist. 

The assumption that mental phenomena are at bottom 
physical in character — special forms of matter or energy — 
may, however, appear to us untenable. It may appear 
that experience compels us to take a Dualistic hypothesis, 
and to assume that mental events form an independent 
series. Nevertheless, since we are still at the standpoint of 
natural science, we shall find in this field also causes 
and effects. This, indeed, is what we must assume if the 
natural science methods of description and explanation are 
to be employed in psychology. So long as psychology sets 
itself the task of regarding mind as made up of a causally 
connected series of events, so long must every mental state 
be regarded as capable of explanation in terms of some 
antecedent process or processes. There can be no state 
that is not determined or conditioned by something outside 
itself. 

Now there is, perhaps, at first sight nothing repugnant 
in a philosophy which interprets the external world as a 
strictly mechanical series of causes and effects. Further 
consideration might, indeed, make it apparent that, if this 
is the ultimate truth regarding the physical world, the mental 
life, through its close and necessary connection with the 
physical, cannot possess any real freedom. It is, however, 
with the natural science account of the mental life itself 
that discontent first arises. The physical world, we are 
likely to feel, may be mechanical: indeed, the mechanical 



§ 96. The Assumptions of the Sciences 399 

view at first sight seems fairly adequate to state what we 
know regarding its behaviour. But the psychological inter- 
pretation of mind as made up of phenomena which are all 
conditioned externally, conflicts directly with our ordinary 
beliefs regarding our own conscious life, and that of our 
fellow-men. If the causal account of mind is ultimate, 
there can, of course, be no freedom or self-determination 
on the part of the individual: the mind is simply the con- 
sciousness of a succession of states which are strictly 
determined in the order and mode of their appearance. 
It seems extremely diflicult to reconcile this interpretation 
of the mental life with what we demand from ourselves 
and others in the life of society, as well as w^ith the sym- 
pathy and interest that we have with motives and acts of 
historical individuals. The scientific view of mind, as made 
up of elements which are conditioned in a purely mechanical 
way in their mode of combination, necessitates a fundamen- 
tally different view of human conduct and of human respon- 
sibility from that usually entertained: it requires us to 
regard our own conduct and that of our fellow-men, not as 
subjects of praise or blame, but simply as phenomena to be 
understood. This is the philosophy of mind and of human 
action at which we arrive when the scientific point of view 
is regarded as the final interpretation. 

96. The Assumptions of the Sciences. — The possibility 
of reaching a different interpretation of the world and of 
experience from that afforded by natural science has been 
more than once suggested in the preceding paragra^phso 
It has never been shown, however, that any other interpre- 
tation is possible. If the account given by the sciences is 
true, how is any other theory possible? Does not a phi- 



400 The Unification of Knowledge 

losophy lose all title to respect which begins by proposing to 
discredit the established results of the sciences ? 

The reply to these objections, is that it is not proposed to 
question the competency of science in its own field; but 
merely to show that, from the very conditions under which 
it is formulated, it cannot supply an answer to the problems 
of philosophy. In other words, the inquiries of the special 
sciences are not directed primarily towards the discovery of 
the ultimate relations of things. Their object is rather to 
discover some method of describing certain groups of phe- 
nomena in such a way as to enable others to apprehend 
them readily and clearly. With this, there is also usually 
connected the practical purpose of determining how the phe- 
nomena can be produced most conveniently, or modified in 
the directions we may desire. Each of the special sciences, 
in other words, takes the point of view and employs the 
conceptions which will enable it to describe most conven- 
iently, in accordance with its own purpose, the group of 
phenomena which constitutes its subject-matter. The vari- 
ous conceptions employed have sometimes been compared 
to instruments or tools which enable the sciences to attain 
the results at which they aim; namely, a systematic descrip- 
tion and correlation of facts. The tests of these conceptions 
from the scientific point of view is found simply in their 
efficiency, or in their capacity to afford a basis for clear 
description and for practical manipulation of the phenomena 
under investigation. ''AH physical ideas and principles,'' 
says Mach, ''are succinct directions, frequently involving 
subordinate directions, for the employment of economically 
classified experiences, ready for use. Their conciseness, 
as also the fact that their contents are rarely exhibited in 



§ 96. The Assumptions of the Sciences 401 

full, often invests them with the semblance of independent 
existence.''^ Moreover, what is here said regarding the 
ideas and principles of physics applies equally to the other 
sciences : in no case are the conclusions derived by employing 
the methods and assumptions which a special science finds ade- 
quate for its purpose to be accepted without modification or 
interpretation, as a direct description of the nature of reality. 
The matter may be put in the following way. All think- 
ing proceeds on the basis of certain assumptions. The most 
general form of these assumptions is expressed by the so- 
called laws of thought as a postulate that the various facts 
that make up our world of experience are to be related 
in a coherent and systematic way. Now, there are various 
ways, more or less adequate, and more or less final, of think- 
ing the relations of things. Although each of the natural 
sciences makes the special assumptions which enable it to 
deal most effectively with the facts in its own field, so that 
its form of explanation always differs in some respect from 
every other, yet all the natural sciences make certain assump- 
tions in common, and therefore may be at first considered 
together in our discussion. The general nature of these 
assumptions we found expressed in the law of causality 
with its corollary, the conception of the uniformity of 
nature. It is plain, therefore, that the conclusions of 
all these sciences is in a sense hypothetical, rather than 
categorical. What they assert is, that if the field of reality 
is defined as composed of phenomena external to one another, 
but standing in strict causal relations, then these laws and 
conceptions appear to express, more adequately than any 
other, the relations of the facts when read from that point of 

^ Popular Scientific Lectures, p. 204. 

2D 



402 The Unification of Knowledge 

view. Statements of this nature are obviously not intended 
to be absolute, or to exclude alternative ways of interpreting 
the facts. The character of the results is evidently con- 
ditioned by the initial assumptions of the whole group of 
natural sciences. 

This point of view may be further illustrated by consider- 
ing its application to some of the special sciences. Mathe- 
matics does not belong to the causal group of sciences whose 
assumptions we have considered; but its hypothetical and 
abstract character is not difficult to realize. The subject- 
matter of mathematics, we say, is not any actually existing 
set of phenomena, but certain ideally simplified forms or 
relations of the real world. The straight line, or the 
triangle, for example, as defined by geometry, are ideal 
conceptions, or hypotheses, from which the science pro- 
ceeds to deduce the consequences. These consequences 
are not taken as direct descriptions of the physical world, 
though they illustrate certain phases or aspects of that 
world. If now we turn to physics, we find that the char- 
acter of the results is determined in the same way, though 
not to the same degree, by the initial definitions and hypoth- 
eses of the science. In order to be able to deal with the 
changing and almost infinite variety of the physical world, 
it is necessary to adopt and carefully define certain concep- 
tions, such as space, time, energy, atom, ether, etc. It 
then becomes the problem of physics to represent all the mani- 
fold phenomena of the external world as determinate rela- 
tions between these conceptions. The choice of these con- 
ceptions is determined by their capacity to correlate facts, 
and to serve as instruments of investigation. In the prog- 
ress of the science, a constant working over and redefining 



§ 96. The Assumptions of the Scieitces 403 

of the working hypotheses goes on, the attempt being always 
to reach conceptions that will be more effective as instru- 
ments of investigation, and at the same time permit of the 
description of phenomena in more concrete terms. 

It follows, then, that the v/orking conceptions of physics, 
no more than the working conceptions of mathematics, are 
exact descriptions of concretely existing things. They are 
ideally simplified conceptions, adopted and defined as effec- 
tive instruments for dealing with the physical world for 
certain purposes. These conclusions are at the present 
time recognized by physicists who are interested in the logical 
interpretation of their results as well as by philosophers. 
A parallel to the following passage from Mach may readily 
be found in the writings of many other writers: ^^When a 
geometer wishes to understand the form of a curve, he first 
resolves it into small rectilinear elements. In doing this, 
however, he is fully aware that these elements are only pro- 
visional and arbitrary devices for comprehending in parts 
what he cannot comprehend as a whole. . . . Similarly, 
it would not be right for physical science to regard its 
self-created, changeable, economical tools, — the molecules 
and atoms — as realities behind phenomena . . . the atom 
must be regarded as a tool for representing phenomena, 
like the functions of mathematics. Gradually, however, 
as the intellect, by contact with its subject-matter, grows 
in discipline, physical science will give up its mosaic play 
with stones and will seek out the boundaries and forms of 
the bed in which the living stream of phenomena flows. 
The goal which it has set itself is the simplest and most 
abstract expression of facts." ^ 

^ Op. cit., p. 206. 



404 The Unification of Knowledge 

In the opening chapter of this book (p. 9) it was stated 
that at the present time an important difference of opinion 
exists as to the proper standpoint and working conceptions 
of the science of psychology. Functional psychology at- 
tempts to employ the principle of purpose or adaptation 
as its principle of analysis and explanation. Structural 
psychology, on the other hand, following more strictly the 
methods of the other natural sciences, describes and explains 
mental life in terms of causally related elements. It is 
this latter view of mind, when accepted without modifi- 
cation as a philosophical theory, to which attention is 
called in the last section. When we reflect on the meaning 
of the results obtained by the natural science method of 
procedure in psychology, it becomes evident that these 
cannot be regarded as furnishing a final or categorical 
account of the real character of the mental life. For, as in 
the case of physics, their form is due to the nature of the 
assumptions adopted by the science. The concrete mental 
life, as we know it in our experience, is a life directed more 
or less consciously, and more or less consistently, to the 
attainraent of certain ends. To live as conscious beings 
means to have purposes, to will certain results, and employ 
ourselves in such a way as to bring about their attainment. 
Without the conception of the mind as a system of func- 
tions, engaged in realizing certain ends, mental life appears 
unmeaning, both from the standpoint of ordinary experience, 
and also from that of sciences like history, ethics, and logic. 
Now, psychology undertakes, in the interest of exact de- 
scription, to exhibit this mental life as a series of causally 
conditioned phenomena, possessing certain definitely ascer- 
tainable characteristics, and taking place in accordance 



§ 97- Philosophy as the hiterpretation of tJie Sciences 405 

with certain laws. In looking at the mental life as made up 
merely of a series of states to be described, psychology neces- 
sarily has to abstract from the function or work of mind. It 
deals only with a certain phase of mind ; or it may be said 
that its results are true only of one side or aspect of the 
total mental life. As science, its results are true and satis- 
factory if they adequately fulfil the purposes of the psy- 
chologist. It is only when they are mistaken for philosophy 
that they become false and misleading. Psychology, as 
Professor Muensterberg has remarked, ^^must not be trans- 
formed into Psychologism. In the preface to his book 
entitled Psychology and Life the same author writes : ''Pop- 
ular ideas about psychology suggest that the psychological 
description and explanation of mental facts expresses the 
reality of our inner experience. It is a natural consequence 
of such a view that our ethical and assthetical, our practical 
and educational, our social and historical views are sub- 
ordinated to the doctrines of psychology. These papers 
endeavour to show that psychology is not at all an expression 
of reality, but a complicated transformation of it, worked 
out for special logical purposes in the service of our life. 
Psychology is thus a special abstract construction which 
has a right to consider everything from its own important 
standpoint, but which has nothing to assert in regard to 
the interpretation and appreciation of our real freedom 
and duty, our real values and ideals." 

§ 97. Philosophy as the Interpretation of the Sciences. — 
The work of philosophy is, however, not fulfilled in simply 
showing that there is no finality in the conclusions of the 
special sciences: there is still demanded, as we have seen, 
such an interpretation of the various facts of experience as 



4o6 The Unification of Knowledge 

will render possible some coherent view of the nature of the 
world as a whole. Now into this construction the results 
of the special sciences must, in some way, enter. These 
results, as has been shown, are hypothetical, abstract, and 
incomplete in character, but they are not arbitrary or capri- 
cious. Although they cannot be taken as directly or cate- 
gorically descriptive of concrete things, scientific proposi- 
tions do illustrate certain general phases or aspects of both 
physical and mental experience, and are therefore significant 
for philosophy. To understand what they really assert, then, 
it is essential to comprehend the limitations and conditions 
which the postulates of the field from which they are derived 
impose upon them. It is only by making clear their assump- 
tions that their true import and significance can be brought 
to light. 

When this has been done, the further problem will remain 
as to what category or conception is most adequate to express 
the relations of all of the various parts of the world of expe- 
rience. What is the highest or final category of thought 
which will prove adequate to the complete unification of 
knowledge? It is clear that the conception which phi- 
losophy aims to define would only be adequate, if it included 
within. itself, as relative or partial truths, the results obtained 
by the investigations of the other sciences. Or, in other 
words, while each of the special sciences, limiting itself, 
as it must, to the investigation of a particular part of the 
world, is never able to obtain the full and final truth about 
that part, its results are never without significance for an 
ultimate synthesis. Indeed, it is only by making use of the 
work of the sciences that philosophy is able to advance to a 
more comprehensive interpretation. On the other hand, 



§ 97- Philosophy as the Interpretation of the Sciences 407 

the sciences are aided in their work of interpreting special 
groups of phenomena by philosophical conceptions regard- 
ing the meaning and bearing of their special results. The 
ultimate postulate of our thought being that the universe 
is systematic and coherent, the part can only be fully compre- 
hended when it is seen in the light of the whole. 

The history of philosophy may be read as an account of 
the attempts made by the human race to find a conception, 
or category, adequate to unify all the facts of experience. 
Beginning with the childlike idea that everything must 
be composed of the same kind of stuff or matter, philo- 
sophical thought quickly advanced to more rational state- 
ments of its problem. At the present time, one may perhaps 
say that the fundamental question in philosophy is whether 
it is possible to employ the category of Teleology or Purposive- 
ness as an explanation of the universe and of our own expe- 
rience; and, if so, what content is to be given to this concep- 
tion. We have noted the fact that an explanation in causal 
terms leads necessarily to an infinite regress (cf. p. 371), 
as well as the other difficulties that arise when this category 
is taken as ultimate. The question then is: Are we jus- 
tified in advancing to a different form of judgment, to judg- 
ments of Teleology or Individuality? (Cf. p. 370.) If 
this question be answered in the affirmative, it is above all 
essential to remember that a change of category is no excuse 
for indefiniteness. Philosophical analysis and interpreta- 
tion are necessarily different from those of science, but 
philosophical procedure must not be less strict than that of 
the sciences, or its conceptions less carefully defined. 



408 The Unification of Knowledge 

REFERENCES 

H. Muensterberg, Psychology and Life, 1899. 

" " The Eternal Values, 1909. 

James Ward, Naturalism and Agnosticism, 2d edition, 1903, espe- 
cially Lectures II.-VI. and XIX. 

E. Mach, Popular Scientific Lectures. 

J. E. Creighton, "Methodology and Truth," Philos. Review, Vol. 
X., pp. 45 ff. 

E. Albee, " The Significance of Methodological Principles," Philos. 
Review, Vol. XV., pp. 267 ff . ; " Descriptive and Normative Sciences," 
Ihid., Vol. XVI., pp. 40 ff. 



QUESTIONS AND EXERCISES 

INTRODUCTION 

Chapter I. — The Standpoint and Problem of Logic 

1. What are some of the main characteristics of thought or 
thinking? Explain the distinction between a subjective and an 
objective account of thought. 

2. Explain the use of the verb to think in each of the following 
sentences: ^I do not know, but I think so;' ^If you think the 
matter over, you will come to the same conclusion.' 

3. 'Words and phrases are often repeated without reflection, and 
their very familiarity is likely to prevent us from attempting to 
understand exactly what ideas they represent.' Give illustra- 
tions of this fact. 

4. What do you mean by science? How does 'scientific' 
knowledge differ from the knowledge of ordinary life ? 

5. What is the meaning of the word 'law' in the phrase 'a law 
of thought'? Compare the use of the word in such expressions 
as 'laws of nature,' 'the laws of the land.' 

6. Is it true that Logic and Psychology have the same subject- 
matter ? 

7. Explain carefully how the problem of Logic differs from 
that of Psychology. 

8. If we parallel Psychology with Morphology, and Logic 
with Physiology, what mental science will correspond to Em- 
bryology ? 

9. Illustrate by means of examples not used in the text the rela- 
tion in which science and art, or theory and practice, stand to 
each other. 

409 



4IO Questions and Exercises 

10. Criticise the following statement: ^ Logic is not only a 
science; it is also an art, for it teaches us to reason correctly.' 

11. What part does Introspection play in investigating logical 
questions ? 

12. In what sense is Logic a ' normative' science? Name other 
sciences that are ^normative.' 

13. In what sense may we say that the records of everything 
which the human race has accomplished form the material of 
Logic ? How does the individual mind deal with this material ? 

Chapter II. — Stages in the Development of Logic 

1. What form did the questions concerning the nature of know- 
ledge first take ? Under what conditions did these first receive defi- 
nite formulation? 

2. ^The sciences have arisen in response to the practical needs 
of mankind.' Is this statement confirmed by the history of the 
origin and development of Logic? 

3. ^ Since each individuak sees things from his own point of 
view, there is therefore nothing really true in itself, or good in 
itself.' Give some illustrations of the former part of this state- 
ment. What term would you use to describe the theory which 
the sentence expresses? 

4. Explain what is meant by the statement that Socrates and 
Plato found a standard of truth and of conduct in the Concept. 

5. Why was it not possible for Aristotle to lay down a complete 
theory of Inductive Reasoning? 

6. Describe the attitude toward Logic during the Middle Ages. 
How can this be accounted for? 

7. What is meant by Bacon's ^method'? In what does its 
value consist? 

8. Describe Mill's services to Logic, also the defects in his 
view of experience. 

9. Describe the standpoint of Modern Logic. 



Questions and Exercises 411 

PART I. — The Syllogism 
Chapter III. — The Syllogism and its Parts 

1. Describe the general purpose and nature of the syllogism. 

2. What is the principle upon which syllogistic reasoning 
depends? Why is it impossible to reason if this principle be 
violated ? 

3. Explain the distinction between the formal and real truth of 
an argument. 

4. Explain the distinction between a Percept and a Concept. 

5. What is meant by the transforming and the conserving 
functions of thought? What part does language play in the 
process of thinking ? 

6. Arrange the following sentences as logical propositions, 
pointing out the logical Subject and the Predicate in each case : — 

(a) Learning taketh away the wildness of men's minds. 

(h) Dissipation wastes health. 

{c) The exposition of a principle indirectly contributes to 

its proof. 
{d) To me the meanest flower that lives can give thoughts 

that do often lie too deep for tears. 
{e) The Alps consist of several parallel ranges. 
(/) The travellers had found the city in ruins. 

7. In the following examples, the student is required (i) to state 
the arguments in syllogistic form, rearranging them if necessary 
in the order of Major Premise, Minor Premise, and Conclusion ; 
(2) to supply missing premises or conclusions, or to condense, 
where several statements really constitute one proposition; (3) to 
state whether the argument seems to be valid : — 

(i) He is not indifferent to money; for he is a sensible man, 

and no sensible man despises money. 
(2) All human productions are liable to error, and therefore 

all books, being human productions, are liable to error. 



412 Questions and Exercises 

(3) All that glitters is not gold; for brass glitters. 

(4) All bodies which move round the sun are planets; there- 

fore the earth is a planet. 

(5) Platinum is a metal, and therefore combines with oxygen. 

(6) Every honest man attends to his business; this person 

attends to his business; therefore this person is an 
honest man. 

(7) Rational beings are accountable for their actions; brutes, 

not being rational, are therefore exempt from re- 
sponsibility. 

(8) I am not mortal, for I have obtained the Elixir Vitce. 

(9) Of course he defends State Rights, for he is a Southerner. 

(10) The poor must be oppressed, for the rich are accumulat- 

ing millions. 

(11) These men are traitors, for they oppose the President. 

(12) It cannot be said that no impractical man is a politician, 

for some politicians are idealists, and no idealist is prac- 
tical. 

(13) Phenomena attributed by savages to the existence of spirits 

are fully capable of explanation by science without this 
hypothesis, therefore the hypothesis ought to be entirely 
discarded. 

(14) Neglect of pleasure is the best way to secure it; for the 

more we aim at pleasure, the less likely we are to get it. 

(15) Restless nations are not progressive, for we see that the 

civilized nations are all progressive, while all the un- 
civilized nations are restless. 

(16) Any citizen may rightly resist a law of which his reason 

disapproves, for every man is in duty bound to follow 
the dictates of his reason. 

(17) Materialism is refuted by the fact that, while all man's 

material qualities may be transmitted by inheritance, 
his knowledge cannot. 



Questions and Exercises 413 

(18) Every one desires money, because every one desires power. 

(19) We must not give in to him, for if you give him an inch, he 

will take an ell. 

(20) Covetous men are not happy, seeing that they are always 

in fear. 

(21) The example of Virgil shows that a great poet may be 

led into some faults by the practice of imitation. 

(22) You must have met him, for you were at the university at 

the same time. 

(23) No strike but injures trade, and consequently impover- 

ishes the country. But this is to diminish the means of 
happiness. And as all that is detrimental to happiness 
is to be condemned, we must absolutely condemn strikes. 

(24) This document cannot be genuine, or it would have been 

referred to by the supposed author^s contemporaries. 

(25) This is too good to be true. 

(26) It is inconceivable that the material world should be per- 

ceived, since we can only perceive that which lies 
within consciousness. 

(27) A great chess-player is not a great man, for he leaves the 

world as he found it. 

(28) It is a mistake to improve the economic condition of the 

inefficient, so we ought not to assist the destitute. 

(29) B is so bad a marksman that the safest place to stand is 

directly in front of the bulPs-eye. (12-29 St. Andrew's.) 

(30) He is already rich and powerful, so that he cannot be guilty 

of usury and extortion. 

(31) Years bring wisdom, but you are still young. (30-31 

Glasgow.) 

(32) The man I don't like is the man I don't know. 

(33) One belated diversion the high-tariff people are now trying 

to make. They betray a sudden anxiety about the 
revenue. . . . But the moment you begin to talk of 



414 Questions and Exercises 

the tariff as needed for revenue, that moment you 
abandon the protectionist point of view. To fix the 
duties at a level where they would produce the greatest 
revenue is a process which has nothing to do with pro- 
tection. Instead of keeping up the rates for the pur- 
pose of bringing in more money, the true way might be 
to cut them in two. 

(34) In this country we yet have a hard road to travel before we 

reach free trade, or even the nearer stage of a tariff 
for revenue only. We are and shall remain large 
producers of grain and meat; and it is therefore un- 
likely that we shall be driven to free trade, as England 
was, by the pangs of the millions. The economic ar- 
gument is still irrefutable; but, while men are earn- 
ing a fair wage, are fed, and comfortably clad and 
housed, they are indifferent to general principles. Too 
many of us hear only the cry of the belly. 

(35) No human being in this country can exercise any kind 

of public authority which is not conferred by law ; and 
under the law of the United States it must be given 
by the express words of a written statute. Whatever is 
not so given is withheld, and the exercise of it is posi- 
tively prohibited. Courts-martial in the army and navy 
are authorized ; they are legal institutions ; their jurisdic- 
tion is limited, and their whole code of procedure is 
regulated by act of Congress. Upon the civil courts 
all the jurisdiction they have or can have is bestowed 
by law, and if one of them goes beyond what is written, 
its action is ultra vires and void. But a military com- 
mission is not a court-martial, and it is not a civil 
court. It is not governed by the law which is made 
for either, and has no law of its own. ... So these 
commissions have no legal origin and no legal name 



Questions and Exercises 415 

by which they are known among the children of men; 
no law applies to them, and they exercise all power for 
the paradoxical reason that none belongs to them 
rightly. (J. S. Black.) 

(36) Has (the constitution) empowered Congress to enact 
what free persons, born within the several states, shall 
or shall not be citizens of the United States ? Before 
examining the various provisions of the constitution 
which may relate to this question, it is important to 
consider for a moment the substantial nature of this 
inquiry. It is, in effect, whether the constitution has 
empowered Congress to create privileged classes within 
the states, who alone can be entitled to the franchises 
and powers of citizenship of the United States. If it 
be admitted that the constitution has enabled Congress 
to declare what free persons, born within the several 
states, shall be citizens of the United States, it must 
at the same time be admitted that it is an unlimited 
power. If this subject is within the control of Congress, 
it must depend wholly on its discretion. For certainly 
no limits of that discretion is found in the constitu- 
tion, which is wholly silent concerning it; and the nec- 
essary consequence is that the federal government may 
select classes of persons who alone can be entitled to 
the political privileges of citizenship of the United 
States. If this power exists, what persons born within 
the states may be president or vice-president of the 
United States, or members of either house of Congress, 
or hold any office or enjoy any privilege whereof citi- 
zenship of the United States is a necessary qualifica- 
tion, must depend solely on the will of Congress. By 
virtue of it . . . Congress . . . may create an oli- 
garchy, in whose hands would be concentrated the en- 



41 6 Questions and Exercises 

tire power of the federal government. . . . Certainly^ 
we ought to find this power granted by the constitution, 
at least by some necessary inference, before we can say 
it does not remain to the states or the people. (B. R. 
Curtis.) 

Chapter IV. — Terms 

I. Distinguish in the following list the terms which are usually 
(i) Singular, (2) General, and (3) Collective. If any term may 
belong to more than one class, explain and illustrate its various 
uses. 



Niagara Falls, 


an oak tree. 


the United States Navy, 


gold, 


a dancing party, 


Brooklyn Bridge, 


chair. 


the United States, 


humanity, ^^*-*i 


a pack of cards. 


city, 


the centre of the earth. 



2. Explain and illustrate the ambiguity in the use of the word 
^alL' 

3. In what two ways are the words Abstract and Concrete 
used? In what sense, if at all, can we say that Psychology and 
Logic are ^abstract' sciences? 

4. What do you think that Hegel meant when he said that ^^it 
is the uneducated man who thinks abstractedly''? 

5. Distinguish carefully between Contradictory and Opposite 
terms. ^ ^- ^^Wx 

6. What are Correlative terms? Give at least three examples. 

7. Mention the synonyms for Intension and Extension. 

8. Explain the Extensional and Intensional use of the following 
terms : — 

metal, chair, man, Caesar, superstition, 

justice, student, John Jones, island, emperor. 

9. Criticise the statement that ^Extension and Intension stand 
in inverse ratio to each other.' What truth does it contain? 



Questions and Exercises x^-^^^ 417 

10. Invent a series of at least six terms which may be arranged \0^ 
so as gradually to increase in Extension. 

11. What may be said in reply to Mill's contention that proper 
names are non-connotative ? 

Chapter V. — Definition and Division ^^ 

1. Why is Definition necessary? 4 '^-'r.:^^ 1^"^^^^^^' * 

2. What is the distinction between extensive and intensive 
definition? What is a verbal definition? 

3. In what two ways may we conceive the problem of Definition ? 

4. What do you understand by the Socratic Dialectic? Ex- 
plain its purpose and mode of procedure. 

5. Explain the terms: — 

genus, differentia, \J>^ infirma species, ^ ^ , , 

species, summum genus, sui generis. e^AA.v^-'^^'' j^>,v> 

6. What various methods or kinds of definition can you dis- 
tinguish? What is it which determines v/hich method shall be 
used in any particular case ? What is genetic definition ? 

7. Criticise the following definitions, pointing out what rules, 
it any, are violated by them, and distinguishing genus and differen- 
tia, if possible, in each : — 

(i) Logic is the science of thought. 

(2) A power is a force which tends to produce motion. 

(3) Tin is a metal lighter than gold. 

(4) A gentleman is a man who has no definite means of 

support. 

(5) The body is the emblem or visible garment of the soul. 

(6) Man is a vertebrate animal. 

(7) Thunder-bolts are the winged messengers of the gods. 

(8) A moral man is one who does not lie or steal or live 

intemperately. 

(9) Cheese is a caseous preparation of milk. .,^5^*-^^ ' 

(10) Evolution is to be defined as a continuous change from 
2 E 



41 8 Questions and Exercises 

indefinite incoherent homogeneity to definite coherent 
heterogeneity of structure and function, through suc- 
cessive differentiations and integrations. (Spencer.) 
(ii) Oats is a grain which in England is generally given to 
horses, but in Scotland supports the people. 

(12) Tickling may be defined as an intensely vivid complex of 

unsteady, ill-localized, and ill-analyzed sensation, with 
attention distributed over the immediate sensory con- 
tents and the concomitant sensations reflexly aroused. 

(13) Panmixia is the fact that " natural selection is required to 

preserve an organ in an active condition as well as to 
produce it, and if this action is withdrawn, the organs 
will degenerate from promiscuous breeding.'' 

(14) Belief is the consequence of an indissoluble association 

of ideas. 

(15) Life is the opposite of death. 

(16) Reverence is the feeling produced by the recognition of 

worth or superiority in others. 

(17) Religion consists in the feeling of absolute dependence. 

(Schleiermacher.) ,i -w. <^ A^-^^ti^ t^j.^^ua^ ^Ti^-- V^ ' ''* 

(18) Religion is a desire manifested by prayer, sacrifice, 

and faith. (Feuerbach.) 

(19) Religion is the sentiment aroused by regarding duty as 

based on a divine command. (Kant.) 

(20) Religion is a faculty of the mind by which, independently 

of the senses and of reason, man is able to perceive 
the Infinite. (Max Mliller.) 

(21) Religion, in its lowest terms, is the belief in spiritual 

beings. (Tylor.) 

(22) Material Goods consist of useful material things, and 

of all rights to hold, or use, or derive benefits from ma- 
terial things, or to receive them at a future time. 
(Marshall.) 



Questions and Exercises 419 

(23) A man's Wealth consists of ( ) those Material Goods to 

which he has (by law or custom) private rights of prop- 
erty, and which are therefore transferable and exchange- 
able; and of (ii) those of his Immaterial Goods which 
are external to him, and serve directly as the means of 
enabling him to acquire ^Material Goods. (Marshall.) 

(24) Or, Wealth includes all those things, external to a man, 

which (i) belong to him, and do not belong equally to 
his neighbours, and therefore are distinctly his; and 
(2) which are directly capable of a money measure. 
ilUd) 

(25) A person's capital is that part of his stock from which he 

expects to derive an income. (A. Smith.) 

(26) A person's capital is that portion of his wealth by which 

he earns his livelihood. (Marshall.) 

(27) Capital is the accumulation of all that is valuable which 

has been withdrawn from unproductive consumption^ 
(Say.) 
{2%) Capital is that portion of the produce of industry which 
can be made directly available to support human exist- 
ence or to facilitate production. (M'Culloch.) 

(29) Capital is something produced, for the purpose of being 

employed as the means toward a further production. 
(Mill.) 

(30) Rent is what is paid for the license to gather the produce 

of the land. (Smith.) 

(31) Rent is that portion of the produce of the earth which is 

paid by the farmer to the landlord for the use of the 
natural and inherent powers of the soil. (M'Culloch.) 

(32) Rent is the difference between the return made to the 

most productive, and that which is made to the least 
productive, portion of capital employed on the land. 
(Mill.) 



420 Questions and Exercises 

(33) Rent is the income derived from the ownership of land 

and other free gifts of nature. (Marshall.) 

(34) Wages is the price of labour. (Smith and many others.) 

(35) Labour is any exertion of mind or body undergone partly 

or wholly with a view to some good other than the 
pleasure derived directly from the work. (Marshall.) 

{^'^6) Vestigial characters in animals are the remnants of past 
adaptations. 

(37) ''By isolation, segregation, or separation as a factor in 
evolution, we mean the failure of a portion of one group 
or species to interbreed freely with the rest of its kind." 
(Jordan.) 

8. Give examples of terms which are indefinable, and explain 
why this is the case. What is the distinction between Descrip- 
tion and logical Definition? 

9. Define the following terms by giving the genus and differ- 
entia : — 

science, republic, psychology, island, 

triangle, monarchy, gold standard, import duty. 

10. Define the following terms in whatever way seems most 
suitable and satisfactory : — 



organism, 


cantilever bridge. 


oxygen. 


steel. 


Natural Selection, 


book. 


indigo blue. 


surd number, 


tyranny, 


parabola. 


torsion, 




tort. 


Communism, 


pain. 





Can any of these be defined in more than one way? 
II. Examine the following Divisions and point out which are 
logical and which are not : — 

(i) Living beings into moral and immoral. 

(2) Men into saints and sinners. 

(3) Religions into true and false. 

(4) Man into civilized and black. 



Questions and Exercises 421 

(5) Geometrical figures into rectilinear and non-rectilin- 

ear. 

(6) Substances into material and spiritual. 

(7) Metals into white, heavy, and precious. 

(8) Elementary mental processes into sensations and affec- 

tions. 

(9) Students into those who are idle, those who are athletic, 

and those who are diligent. 
(10) Books into scientific and non-scientific. 



Chapter VI. — Propositions 

1. What is a proposition ? In what sense may a proposition 
be said to have parts ? 

2. Distinguish between Categorical and Conditional propo- 
sitions. 

3. What is meant by {a) the Quality, and (&) the Quantity, of 
propositions ? 

4. Arrange the following sentences in the form of logical propo- 
sitions, and indicate the Quality and Quantity of each categorical 
proposition by the use of the letters A, E, I, and O : — 

p:) Brevity has to be sought without sacrificing perspicuity. 
^ (2) He that doeth these things is like to a man that buildeth 

his house upon a rock. 
^ "(3) Socrates declared knowledge to be virtue. 
- (4) Phosphorus does not dissolve in water. 
4(5) Nearly all the troops have left the town. 
^\ (6) Only ignorant persons hold such opinions. 
--^^T^iji) Few persons are proof against temptation. 

C:i^) Over the mountains poured the barbarian horde. 

(9) Fine words butter no parsnips. 
(10) Logic is only common sense formulated. 

5. How does formal logic interpret the relation between the 



422 Questions and Exercises 

subject and predicate of a categorical proposition ? Does this 
view do full justice to the signification of propositions ? 

6; How would you represent by means of circles the proposition,^ 
'gold is the most precious metal' ? 

7. What do you mean by the distribution of terms ? Explain 
why negative propositions distribute the predicate, while affirma- 
tive propositions do not. 

8. State precisely what is asserted by Proposition I. What 
forms may the diagrams which represent this proposition assume ? 

Chapter VII. — The Interpretation of Propositions 

1. Why is it better to speak of the Interpretation of proposi- 
tions than to use the term 'Immediate Inference'? 

2. What is meant by the Opposition of propositions? 

3. Explain the distinction between Contrary and Contradic- 
tory propositions. 

4. If proposition O is false, what is known regarding the truth 
or falsity of A, E, and I? 

5. What is the simplest proposition which must be established 
in order to disprove the following statements : {a) All men desire 
wealth, (h) No man is perfectly happy, {c) Some knowledge 
is not of any value, {d) Pain alone is evil, {e) All is not lost. 

6. Give the contrary (or sub-contrary), and the contradictory 
of: {a) All metals are elements, {h) No coward need apply. 
{c) Socrates was the wisest man in Athens, {d) Not all men are 
brave, {e) No man but a traitor would have done this. 

7. Give the Obverse and, in the cases where it is possible, the 
Inverse, of the following propositions : — 

(i) All horses are quadrupeds. 

(2) Good men are charitable. 

(3) None of the captives escaped. 

(4) Some of the planets are not larger than the earth. 

(5) Some students do not fail in anything. 



Questions and Exercises 423 

(6) All English dukes are members of the House of Lords. 

(7) No illogical author is truly scientific. 

8. Convert in at least one way: — 
(i) All men are rational. 

(2) Some metals are readily fusible. 

(3) Perfect happiness is impossible. 

(4) None of the captives escaped. 

(5) Uneasy lies the head that wears a crown. 

(6) Not every man could stand such hardships. 

(7) None but the brave deserve the fair. 

(8) Phosphorus will not dissolve in alcohol. 

(9) Hydrogen is the lightest body known. 
(10) The world is my idea. 

9. Convert by contraposition : — 

(i) All honest men are of this opinion. 

(2) Oxygen can be prepared by heating potassium chlorate 

in a thin glass flask. 

(3) Some of the enemy were not prepared to surrender. 

(4) Not all who came to scoff remained to pray. 

(5) A triangle is a plane figure bounded by three straight 

lines. 

(6) The return of peace had given fresh confidence to the 

government party. 

10. Describe the logical relation between each of the four 
following propositions : — 

(i) All substances which are material possess gravity. 

(2) No substances which possess gravity are immaterial. 

(3) Some substances which are immaterial do not possess 

gravity. 

(4) Some substances which do not possess gravity are im- 

material. (Jevons.) 

11. What is the Obverse of the Converse of, 'None of the planets 
shine by their own ligh't'? 



424 Questions and Exercises 

12. Can we logically conclude that because heat expands bodies, 
therefore cold contracts them? (Jevons.) 

13. What is the logical relation, if any, between the two asser- 
tions in Proverbs xi. i, ^A false balance is an abomination to the 
Lord; but a just weight is his delight'? (Jevons.) 

Miscellaneous Exercises in Propositions 

In the case of each of the single propositions following, it is 
suggested that the student first state it in strict logical form, clas- 
sifying it as A, E, I, or O, and then give, in the order named, its 
Contrary (or Sub-contrary), Contradictory, Subaltern (or Superior), 
Converse, Obverse, and, in case it has any, Contrapositive and 
Inverse. 

The other questions are self-explanatory. 

1. Not all are free who mock their bonds. 

2. Work that cannot be paid for is alone worth doing. 

3. Ability and indolence are not entirely incompatible. 

4. In the multitude of counsellors there is wisdom. 

5. Not all non-intoxicants are harmless. (St. Andrews.) 

6. Necessity knows no law. 

7. The meekest of men may be incited to violence. 

8. All men are at times actuated by unselfish motives. 

9. Science is not any particular or chance body of facts. 

10. The theory of evolution is not confined to biology. 

11. Theologians are far from unanimity in their attitude toward 
theology. 

12. All lawyers are not formalists. 

13. Some men have no taste for literature. 

14. Examine the following argument: — 

If proposition O be true, I may be true ; if I may be true, A may 
be true: .*. if O be true, A may be true. (St. Andrews.) 

15. All probable events are possible. 



Questions and Exercises 425 

16. All parallel lines are lines which do not meet. 

17. No one who is not a taxpayer can vote in this election. 

18. What can't be cured must be endured. 

19. All bacteria are not harmful. 

20. Whatever is, is right. 

21. Some citizens are not eligible to the presidential office. 

22. Four years of study is required for a degree. 

23. A point has no magnitude. 

24. Conscience is capable of becoming more than the hand- 
maid of the law. 

25. Philosophy bakes no bread. 

26. Does the second of these propositions follow from the first, 
and, if so, what is the logical relation between them ? 

{a) Things equal to the same thing are equal to each other. 
(6) Things not equal to each other are not equal to the same 
thing. 

27. No wise man runs into danger needlessly. 

28. All warm-blooded animals are air-breathers. 

29. Some criminals are well-educated men. 

30. No triangle has one side equal to the sum of two others. 

31. The line which bisects the vertical angle of an isosceles tri- 
angle bisects the base. 

32. Only those who have never felt a wound jest at scars. 

33. Assuming that ^ All monochromatic light is coloured, ' what 
can you conclude as to the truth or falsity of the following proposi- 
tions, monochromatic and mixed, and coloured and white, being con- 
tradictories ? 

(a) No mixed light is coloured. 

(h) Some coloured light is not mixed. 

{c) All coloured light is mixed. 

{d) Some white light is monochromatic. 

(e) Some mixed light is not white. 



426 Questions and Exercises 

34. If ^ All who are happy are wise/ does it follow that ^AU 
who are foolish are unhappy'? (Glasgow.) 

35. What is not practicable is not desirable. 

36. Cursed is every one that hangeth on a tree. 

37. All's well that ends well. 

'^Z. All cannot receive this saying. 

39. There are studies much vaunted and yet of little utility. 

40. All the men who do not row play ball. 

41 . Not to know me argues thyself unknown. 

42. There is ho folly of which he is not capable. 

43. One man is as good as another. 

44. If a man is not good, he cannot be happy. 

45. Every man is not his own master. 

46. Honesty is not always the easiest policy. 

47. It is not possible to predict events without knowing their 
true cause. 

48. Unasked advice is seldom acceptable. 

49. All are not happy that seem so. 

50. Few men reason, but everyone argues. 

51. No man is poor that does not think himself so. 

52. Every industrious man is not well employed. (St. Andrews.) 

53. Criticise the following : — 
Granted that it is true that, 

All wise men are mortal, 
then. No wise men are immortal, 
and, No immortal beings are wise men. 
Hence it is false that. 

Some immortal beings are wise men, 
and that. Some immortal beings are not unwise men. 
But if this is false, it must be true that. 

All immortal beings are unwise men, 
and that, Some unv/ise men are immortal beings. 



Questions and Exercises 427 

54. Fine art is thought suffused with emotion. 

55. No lifeless body has power to change its own state of motion. 

56. No one is free who is enslaved by his own desires. 

57. All that glitters is not gold. 

58. Few men of taste or intelligence are found among the very 
rich. 

59. No one can be successful who is not both studious and 
ambitious. 

60. All the judges but two condemned the prisoner. 

61. ^ No psychosis without neurosis; no neurosis without psy- 
chosis. ' Does the truth of the first half of this statement involve 
that of the second? 

62. Every mistake is not a proof of ignorance. 

63. Not all the metals are heavier than water. 

64. One bad general is better than two good ones. 

65. In man there is nothing great but mind. 

66. Not every man could stand such exposure. 

67. I shall not all die. 

68. State the relation between the three propositions contained 
in the following sentence : ^ The voluntary muscles are all striped, 
and the unstriped muscles are all involuntary, but a few of the 
involuntary muscles are striped. ' 

69. 'Tis cruelty to load a falling man. 

70. If it is true that there is ^No faith without works,' does 
it follow that the doing of works proves that faith is present ? 

71. State the relation between 
ip) Good men are wise. 

(&) Unwise men are not good. 

(c) Some unwise men are good. 

(d) No good men are unwise. 

72. Philosophers in many instances do not avoid mistakes. 

73. All who have nothing m which to interest themselves are 
unhappy. 



428 Questions and Exercises 

J4, You cannot be just, if you are not humane. 

75. Few of us are not in some way infirm. 

76. All our mistakes are not borne by ourselves. 

77. Only the young prefer bravado to experience. 

78. Only the impartial reason. 

79. All seeds do not contain albumen. 

80. Few candidates were satisfactory. 

81. The burnt child dreads the fire. 

82. No one who presented himself failed to pass. 
8^, Only the wise are prudent. 

84. A friend in need is a friend indeed. 

85. Some victories are worse than defeats. 

86. There is none virtuous, no, not one. 

87. No one can be rich and happy unless he is also prudent 
and temperate, and not always then. 

88. No child ever fails to be troublesome, if ill-taught and 
spoiled. 

89. Many a rose is born to blush unseen. 

90. All emotions are compound mental states. 

91. It's an ill wind that blows good to nobody. 

92. Some laws arise from custom. 

93. Not all who are called are chosen. 

94. He envies others' wealth who has none himself. 

95. Only doctors understand this subject. 

96. If it is true that ^Students who do their work faithfully 
should receive university credit,' does it follow that ^Students 
should receive university credit for a faithful effort to do their 
work ' ? 

97. A few Greeks vanquished the vast army of Darius. 

98. Only ignorant persons hold such opinions. 

99. If it is true that ^ There is no disgrace in losing when one 
has done one's best,' does it follow that ^ Those who win deserve 
no particular glory ' ? 



Questions arid Exercises 429 

100. If certain admirable qualities, such as concentration, the 
capacity for hard work, and persistence, will carry a man no 
farther than tenth in his class, does it follow that the first nine 
places can be won only by men without concentration, persistence, 
or the capacity for hard work? {N .Y . Evening Post.) 

10 1. Since 'Hottentots are men,' can we say that a clever 
Hottentot is a clever man? 

102. In the case of the proposition ^All wise acts are honest 
acts,' answer the following questions: (a) How is its converse 
related to its subaltern? {h) How is its converse related to the 
converse of its. subaltern? {c) How is its subaltern related to 
its contradictory? (Jevons.) 

103. Name the logical process by which we pass from each of 
the following propositions to the succeeding one : — 

{a) All metals are elements. 

(&) No metals are non-elements. 

{c) No non-elements are metals. 

{d) All non-elements are non-metals. 

{e) All metals are elements. 

(/) Some elements are metals. 

{g) Some metals are elements. (Jevons.) 

104. None but a logical author is a truly scientific author. 

Chapter VIII. — The Syllogism and its Rules 

1. What is the relation of the Proposition and the Syllogism? 

2. What is the function of the Middle Term in a Syllogism? 

3. How are the major and minor terms, and the major and 
minor premises of a Syllogism distinguished ? 

4. Prove the seventh and eighth canon of the Syllogism, {a) by 
means of the previous rules, and (h) by the use of circles. 

5. Construct an argument to illustrate the fallacy of ambigu- 
ous middle term. 

6. Arrange the following arguments in the regular logical 



430 Questions and Exercises 

order of major premise, minor premise, and conclusion, and 
examine them to see whether they conform to the canons of the 
Syllogism:— ^ ^ ^^^, 

(i) Gold is not a compound substance; for it is a metal, 

^ and none of the metals are compounds. v^^*^\^ 
..(2)' All national holidays are bank holidays, the bank will 
therefore be closed on the Fourth of July. ' ■ v^*m»-*^-o 

(3) All cruel men are cowards, no college men are cruel, 

therefore no college men are cowards. 

(4) Some useful metals are becoming rarer. Iron is a useful 

metal, a,hd is therefore becoming rarer. 

(5) This man shares his money with the poor, but no thief 

ever does this, therefore this man is not a thief. 

(6) He who is content with what he has is truly rich. An ^ 

envious man is not content witl^i what he has; no en- 
vious man therefore is truly rich. 
7. What does the Figure of an Argument depend upon? How 
do you distinguish the four figures? 

Chapter IX. — The Valid Moods and the Reduction of Figures 

1. Arrange the following arguments in logical order, and give 
the mood and figure in each case : — 

(i) No P is M, (2) All M is S, 

Some S is M, ■ , Some M is P, 

Therefore some S is not P. Therefore some S is P. 

2. Name the premises from which valid conclusions may be 
drawn, no account being taken of figures : — 

AA, EO, lA, 10, II, EE, EI, AE, EA, OO. 

3. Prove the special canons of the fourth figure. 

4. ' The middle term must be distributed once at least. ' In 
what figures may it be distributed twice? What is the character 
of the conclusion when this occurs ? 



Questions and Exercises 431 

5. Prove generally that when the major term is predicate in its 
premise, the minor premise must be affirmative. 

6. If the major term be distributed in its premise, but used undis- 
tributively in the conclusion, determine the mood and figure. 

7. Explain why we can obtain only negative conclusions by 
means of the second figure and particular conclusions by means of 
the third figure. 

8. What conclusions do AA, AE, and EA, yield in the fourth 
figure ? Explain. 

9. Is it possible for both major and minor terms to be particular 
at the same time in the premises? If so, construct an argument 
where this is the case. 

10. What do you understand by Reduction? Reduce the 
following argument to the first figure: — 

No fixed stars are planets, 

All planets are bright and shining, 

Therefore some bright and shining bodies are not fixed stars. 

Chapter X. — Abbreviated and Irregular Arguments 

1. Complete the following arguments, determine their mood 
and figure, and examine them to see if they violate any of the rules 
of the syllogism : — 

V (i) Blessed are the meek, for they shall inherit the earth. 
(2) He must be a strong man ; for he was on the crew. 
^ (3) Zoophytes have no flowers ; therefore they are not plants. 
^J^ ^)'None but material bodies gravitate; therefore air is a 
r^ material body. 

, , . (^) He has been a politician for years, and is therefore not 
^ ^JX:¥% be trusted. 

2. Illustrate the difference between the Progressive or Synthetic, 
and the Regressive or Analytic, methods as employed in Mathematics 
and Pyschology. May a science employ both methods at the same 
time ? 



432 Questions and Exercises 

3. Break up the concrete examples of Sorites given on pages 136, 
137, into syllogisms. 

4. Show generally why all the premises except the first in the 
Aristotelian Sorites must be universal. 

5. Prove that in the Goclenian Sorites the first premise alone 
can be negative, and the last alone particular. 

6. In the examples of arguments given on page 139, is there 
any middle term? If not, what serves as the standard of com- 
parison ? 

7. What is the general principle on which all a fortiori arguments 
proceed ? How can you tell when an argument is of this type ? 

8. State the argument implied in the following : — 

*If a man love not his brother whom he hath seen, how shall 
he love God whom he, hath not seen?' 



Chapter XI. — Hypothetical and Disjunctive Arguments 

1. What reasons are there for classifying the disjunctive propo- 
sition as conditional ? 

2. What are the rules of the hypothetical syllogism? 

3. Is it ever possible to obtain a valid conclusion by denying 
the antecedent or affirming the consequent ? 

4. Determine which of the following hypothetical arguments are 
valid and which invalid ; then express the latter in the categorical 
form pointing out what are the categorical fallacies which result : — 

(i) If a man is avaricious, he will be unhappy; but A is 
unhappy, and we may therefore conclude that he is 
avaricious. 

(2) If A is B, C is D; but A is B, therefore we may conclude 

that C is D. 

(3) If the door were locked, the horse would not be stolen ; 

but the horse is not stolen, therefore the door must 
have been locked. 



Questions and Exercises 433 

(4) If man were not capable of progress, he would not differ 

from the brutes ; but man does differ from the brutes, 
therefore he is capable of progress. 

(5) If he had studied his lesson, he would have been able to 

recite ; but he was able to recite, and therefore must 
have studied his lesson. 

(6) If it becomes colder to-night, the pond will be frozen over ; 

but it will not become colder to-night, therefore the 
pond will not be frozen over. 

5. What aspects of thinking are emphasized by the categorical 
and hypothetical forms of reasoning respectively ? 

6. How far may the disjunctive proposition be regarded as 
an expression of ignorance, and what is the justification for the 
statement that it involves systematic knowledge? 

7. To what fallacy is the disjunctive argument specially liable? 

8. How would you criticise the dilemmatic arguments given on 
page 158? 

9. State the following fully as a dilemma: — 

^ There are two kinds of things which we ought not 10 fret about; 
what we can help, and what we cannot. ' (Whately.) 

10. ^When men are pure, laws are useless; when men are cor- 
rupt, laws are broken.' (Jevons.) 

State the above fully as a dilemma, and construct a counter- 
dilemma in rebuttal. \ 

Chapter XII. — Fallacies of Deductive Reasoning 

1. What is the distinction between errors of interpretation and 
fallacies in reasoning? 

2. Why is the detection of material fallacies a proper subject 
of logic ? 

3. If it is true that ^ all the righteous people are happy,' can 
we conclude that ' all unhappy people are unrighteous ' ? If so, 
how do we pass from the first statement to the second ? 

2r 



434 Questions and Exercises 

4. Can we proceed logically from the proposition, 'all good 
citizens vote at elections/ to 'all who vote at elections are good 
citizens ' ? 

5. Does the statement that 'some sciences are useful/ justify 
the proposition that 'some useful things are not sciences'? 

6. Mention the fallacies of Equivocation, and explain what is 
common to them all. -.^^w^^'^^ ..4m^ - 

7. Explain the terms: Petitio Principii, Circulus in probanda ^ 
Argumentum ad hominem, Argumentum ad populum. 

8. Examine the following reasoning: 'The argument from 
design must be regarded as without value; for it has been re- 
jected by Spinoza, Kant, Spencer, and Darwin.' 

9. Point out and name the fallacy or fallacies in the following : — 
(i) We know that God exists because the Bible tells us so; 

and we know that whatever the Bible affirms must be 
true, because it is of Divine origin. (Edinburgh.) 

(2) This is a dangerous doctrine, for we find it upheld 

by men who avow their disbelief in Revelation. 
(Jevons.) 

(3) He must be a Mahometan, for all Mahometans hold 

these opinions. (Edinburgh.) 

(4) It is not right for you to devote all your^time to archae- 

ological research, for if all men did so, the business 
of the world could not go on. (Boyce Gibson.) 

(5) Every incident in this man's account of the affair is 

natural and probable, and we may therefore regard 
his story as quite possibly true. (Jevons, modified.) 

(6) Great men have been derided, and I am derided ; which 

proves that my theory ought to be adopted. (De 
Morgan.) 



Questions and Exercises 435 

Miscellaneous Examples of Deductive Arguments 

Arrange the following arguments whenever possible in regular 
logical order, supplying premise or conclusion where either is 
lacking, or condensing when several sentences are used to state 
one proposition; determine whether or not the arguments are 
valid; f 'give" the mood and figure of the valid categorical argu- 
ments ;y if any argument is invalid, point out and name the fallacy 
involved : — 

1. All virtue is praiseworthy, and charity is a virtue; therefore 
charity is praiseworthy. 

2. All colours are physical phenomena; but no sound is a 
colour, therefore no sound is a physical phenomenon. 

3. Some minerals are precious stones, all topazes are precious 
stones; therefore some minerals are topazes. 

4. Some acts of homicide are laudable; therefore some cruel 
things are laudable. 

5. If he has found the treasure, he is rich ; but he has not found 
it; therefore he is not rich. 

6. He must be a Democrat; for all the Democrats believe in 
Free Trade. 

7. The receiver of stolen property should be punished; you 
have received stolen property, and should therefore be punished. 
(Glasgow.) 

8. Whoever believes this is a heretic; so that you are no heretic, 
for you do not believe this. (Glasgow.) 

9. Good men write good books ; this is a good book, and there- 
fore its writer was a good man. (Glasgow.) 

10. No man desires pain, and without pain your friend's 
cure is impossible; therefore he will not- desire to be cured. 
(Glasgow.) 



436 Questions and Exe^xises 

11. Nothing real is irrational. Everything unreal is transitory. 
Therefore all irrational things are transitory. (St. Andrews.) 

12. Language is the communication of information by signs, 
and so we must say that the wagging of a dog's tail is language. 
(St. Andrews.) 

13. If only the ignorant despise knowledge, this man cannot 
be ignorant, for he praises it. (Edinburgh.) 

14. Whatever is given on the evidence of sense may be taken 
as a fact; the existence of God, therefore, is not a fact, for it is 
not evident to sense. (St. Andrews.) 

15. This explosion must have been occasioned by gunpowder; 
for nothing else would have possessed sufficient force. 

16. This burglary is the work of a professional; for an amateur 
would not have been half so clever. 

17. No stupid person can become President of the United 
States; therefore Mr. Cleveland and Mr. McKinley must both 
have been men of ability. 

18. Since almost all the organs of the body have some use, 
the vermiform appendix must be useful. 

19. Every candid man acknowledges merit in a rival, every 
learned man does not do so; therefore learned men are not 
candid. 

20. Every book is liable to error, every book is a human pro- 
duction, therefore all human productions are liable to error. 

21. Learned men sometimes become mad; but, as he is not 
learned, there is no danger of his sanity. 

22. If this candidate used money to secure his election, he 
deserved defeat ; but he did not use money in this way, and there- 
fore did not deserve defeat. 

23. All valid syllogisms have three terms; this syllogism is 
therefore valid, for it has three terms. 



Questions and Exercises 437 

24. No persons destitute of imagination are true poets ; some 
persons destitute of imagination are good reasoners; therefore 
some good reasoners are not true poets. 

25. Only material bodies gravitate; ether does not gravitate. 

26. In reply to the gentleman's arguments, I need only say 
that two years ago he advocated the very measure which he now 
opposes. 

27. Haste makes waste, and waste makes want; therefore 
a man never loses by delay. (Glasgow.) 

28. C is not D, for A is B; and I know that whenever A is 
not B, C is D. (Glasgow.) 

30. The existence of sensations consists in being perceived; 
all objects are really collections of sensations; therefore, their 
existence consists in being perceived. (Glasgow.) 

31. None but utilitarians are hedonists; practical men are 
utilitarians; therefore they are hedonists. (Glasgow.) 

32. If he claims that he did not steal the goods, why, I ask^ 
did he hide them, as no thief ever fails to do ? 

33. If this therefore be absurd in fact and theory, it must also 
be absurd in idea, since nothing of which we can form a clear 
and distinct idea is impossible. (Hume, Treatise of Human 
Nature.) 

34. Whatever is produced without a cause is produced by 
nothing, or in other words has nothing for its cause. But nothing 
can never be a cause. Hence every object has a real cause of 
its existence. (Hunie, Treatise,) 

35. Everything must have a cause; for if anything wanted 
a cause it would produce itself, that is, exist before it existed, 
which is impossible. (Hume, Treatise). 

36. If it be true, as Mr. Spencer thinks, that the past expe- 
rience of the race has produced innate ideas and feelings, Weis- 
mann's denial of Use-inheritance would be refuted. Certainly, 
but it is just possible that Mr. Spencer's theory is not true. 



438 Questions and Exercises 

37. Democracy is not a perfect form of government, for under 
it there are able men who do not get power; and so it allows 
men to get power who are not able. 

2^"^, Of university professors, some are zealous investigators, 
and some good teachers. A is an excellent teacher, and we 
may therefore conclude that he is not a zealous investigator. 

39. Seeing that abundance of work is a sure sign of industrial 
prosperity, it follows that fire and hurricane benefit industry, 
because they undoubtedly create work. (St. Andrews.) 

40. I will have no more doctors; I see that all of those who 
have died this winter have had doctors. (St. Andrews.) 

41. If a man is educated, he does not want to work with 
his hands; consequently, if education is universal, industry will 
cease. (London.) 

42. Show why IE is an impossible mood in all the figures of the 
syllogism, while EI is possible in all of them. (Glasgow.) 

43. If acquired variations are transmitted, there must be some 
unknown principle of heredity; if they are not transmitted, there 
must be some unknown factor of evolution. (Osborn.) 

44. Some plant-products harmful to insects are not a pro- 
tective development; for all tannin is harmful to insects, 
and most certainly not all tannin is a protective development. 
(St. Andrews.) 

45. Art is not fostered by money; for a true artist would practise 
his art for its own sake, and a bad artist should not be encouraged. 
(St. Andrews.) 

46. The spectra of compound bodies become less complex with 
heat; but the spectra of the elements do not, since they are not the 
spectra of compound bodies. (St. Andrews.) 

47. What can you tell about a valid syllogism if you know: — 
(i) that only the middle term is distributed; (2) that only the 



Questions and Exercises 439 

middle and minor terms are distributed; (3) that all three terms 
are distributed? (Glasgow). 

48. None but the wise are good, and none but the good are 
happy; therefore none but the wise are happy. (Edinburgh.) 

49. Giving advice is useless. For either you advise a man 
what he means to do, in which case the advice is superfluous ; or 
you advise him what he does not mean to do, and the advice is 
ineffectual. (London.) 

50. No pauper has a vote ; AB is a not a pauper, therefore he 
has a vote. (St. Andrews.) 

51. The love of nature is never found either in the stupid or the 
immoral man, therefore stupidity and virtue are incompatible. 
(Edinburgh.) 

52. Not all educated persons spell correctly; for one often finds 
mistakes in the papers of University students. 

53. Free Trade is a great boon to the workingman; for it 
increases trade, and this cheapens articles of ordinary consumption ; 
this gives a greater purchasing power to money, which is equiva- 
lent to a rise in real wages, and any rise in real wages is a boon to 
the workingman. 

54. The figure of Tell cannot be historic, else he must have been 
mentioned by early historians, or his personality would be necessary 
to explain known facts of history. (St. Andrews.) 

55. Nerve power does not seem to be identical with electricity; 
for it is found that when a nerve is tightly compressed nervous 
action does not go on, but electricity can nevertheless pass. 
(Jevons.) 

56. Carbon, which is one of the main sources of the nourishment 
of plants, cannot be dissolved in water in its simple form, and can- 
not therefore be absorbed in that form by plants, since the cells 
absorb only dissolved substances. All the carbon found in plants 
must consequently have entered them in a form soluble in water, 
and this we find in carbonic acid. (Adamson, Jevons.) 



440 Questions and Exercises 

57. No punishment should be allowed for the sake of the good 
that may come of it; for all punishment is an evil, and we are not 
justified in doing evil that good may come of it. (Edinburgh.) 

58. Prove that when the minor term is predicate in the minor 
premise of a syllogism, the conclusion cannot be A. (Glasgow.) 

59. We must be guided by the decisions of our ancestors, for 
old age is wiser than youth. (Oxford.) 

60. If education is popular, compulsion is unnecessary; if 
unpopular, compulsion will not be tolerated. (Oxford.) 

61. Wealth is in proportion to value, value to efforts, efforts 
to obstacles; therefore wealth is in proportion to obstacles. 
(Jevons.) 

62. If the train is late, I shall miss my appointment; if it is 
not late, I shall not reach the depot in time to go by it ; therefore, 
in any case, I shall miss my appointment. 

63. He Vv^ho spareth the rod hateth his child; the parent who 
loves his child therefore spareth not the rod. 

64. Whatever tends to withdraw the mind from pursuits of a 
low nature deserves to be promoted; classical learning does this, 
since it gives us a taste for intellectual enjoyments; therefore it 
deserves to be promoted. 

65. As against the proposition that the formation of pubHc 
libraries prevents private individuals from purchasing, and so de- 
creases the sale of books, a writer urges that whatever encourages 
the reading of books encourages the buying of books. It is a 
library's purpose to encourage reading, and hence the net result 
is rather to increase than to lessen purchases. 

66. The express train alone does not stop at this station, and, 
as the last train did not stop, it must have been the express train. 
(Glasgow.) 

67. The infliction of pain is sometimes justifiable; for a just 
punishment always involves pain. (Glasgow.) 



Questions and Exercises 441 

68. ''The truth is, that luxury produces much good. A man 
gives half a guinea for a dish of green peas ; how much gardening 
does this occasion ?" (Dr. Johnson.) 

69. Protective duties should be abolished; for they are injurious 
if they produce scarcity, and they are useless if they do not. (Ox- 
ford.) 

70. Animals only are sentient beings; all plants are insentient. 
(St. Andrews.) 

71. Only native-born citizens are eligible to this office; but as 
you have this qualification, you need not hesitate to run for it. 
(St. Andrevv^s.) 

72. A primary election law is necessary, for at present the 
people have no voice in the nomination of candidates for office. 

73. I do not see how Mr. Rhodes can escape censure. If he 
knew of Dr. Jameson's raid, he was guilty of complicity; if he 
did not, of negligence. (St. Andrews.) 

74. Business enterprises are most successful when managed by 
those who have a direct interest in them; therefore enterprises 
carried on by the State are not likely to succeed. 

75. All P is M; All S is M; therefore Some not-S is not-P. 
(Glasgow.) 

76. Wherever ideas have become indissolubly associated, it is 
beyond our power to represent them separately; our attitude is 
that of belief. Belief then may be defined as the consequence of 
an indissoluble association of ideas. (Glasgow.) 

77. No reason, however, can be given why the general happiness 
is desirable, except that each person, so far as he believes it to be 
attainable, desires his own happiness. This, however, being a 
fact, we have not only all the proof v/hich the case admits of, but 
all which it is possible to require, that happiness is a good, that 
each person's happiness is a good to that person, and the gen- 
eral happiness, therefore, a good to the aggregate of all persons. 
(Mill's Utilitarianism.) 



442 Questions and Exercises 

78. This man is a Protestant; for he exercises the right of 
private judgment. 

79. If the orbit of a comet is diminished, either the comet passes 
through a resisting medium, or the law of gravitation is partially 
suspended. But the second alternative is inadmissible. Hence 
if the orbit of a comet is diminished, there is present a resisting 
medium. 

80. How do we know that our intuitive beliefs concerning the 
world are invariably true? Either it must be from experience 
establishing the harmony, or an intuitive belief must certify the 
correctness. Now experience cannot warrant such harmony 
except in so far as it has been perceived. Still more futile is it to 
make one instinctive belief the cause of another. Thus we cannot 
know that any intuitive belief is universally valid. (Bain.) 

* 81. Which of the following are real inferences? (i) ^This weighs 
that down, therefore it is heavier'; (2) ^This piece of marble is 
larger than that, and therefore is heavier.' 

82. The parts of pure space are immovable, which follows 
from their inseparability, motion being nothing but change of 
distance between any two things; but this cannot be between 
parts that are inseparable, which therefore must be at perpetual 
rest one amongst another. 

83. All civilized peoples are progressive; all uncivilized peoples 
are superstitious; therefore some superstitious peoples are not 
progressive. (St. Andrews.) 

84. Ignorance is no crime ; and as you did not know what you 
were doing, you should not be punished. (St. Andrews.) 

85. He could not face bullets on the field of battle, and is there- 
fore a coward. (St. Andrews.) 

86. If a man be rightfully entitled to the produce of his labour, 
then no one can be rightfully entitled to anything which is not the 
produce of his labour. (St. Andrews.) 



Questions and Exercises 443 

87. In moral matters we cannot stand still; therefore he who 
does not go forward is sure to fall behind. (Glasgow.) 

^^. A man that hath no virtue in himself ever envieth virtue in 
others; for men's minds will either feed upon their own good or 
upon others' evil ; and who wanteth the one will prey upon the 
other. (Glasgow.) 

89. A successful author must be either very industrious or very 
talented : Gibbon was very industrious, therefore he was not very 
talented. ( Glasgow.) 

90. He who calls you a man speaks truly; he who calls you a 
fool calls you a man; therefore he who calls you a fool speaks 
truly. (Glasgow.) 

91. If a body moves, it must move either in the place where it is, 
or in the place where it is not. But a body cannot move in the 
place where it is, nor yet in the place where it is not. Hence a 
body cannot move at all. 

92. We have no perfect idea of anything but a perception. A 
substance is entirely different from a perception. We have there- 
fore no idea of substance. (Hume.) 

93. Every good government promotes the intelligence of the 
people, and no despotism does that. (Bain.) 

94. He was too impulsive a man not to have committed many 
errors. (Bain.) 

95. A true philosopher is independent of the caprices of fortune, 
for he places his chief happiness in moral and intellectual excellence. 

96. Educated among savages, he could not be expected to know 
the customs of polite society. (Bain.) 

97. No war is long popular; for every war increases taxation, 
and the popularity of anything that touches our pockets is very 
short-lived. 

98. There can be no such thing as an omniscient mind, since all 
thinking is a succession of mental states. (St. Andrews.) 



444 Questions and Exercises 

99. Morality is either superfluous or unavailing, according as the 
universe is righteous or not. (St. Andrews.) 

100. The earth's position must be fixed, if the fixed stars are 
seen at all times in the same situations ; now the fixed stars are 
not seen at all times in the same situations; therefore the earth's 
position is not fixed. (Edinburgh.) 

loi. The table we see seems to diminish as we move from it; 
but the real table suffers no change; it was not, therefore, the 
table itself, but only its image, that was present to the mind. 
(Jevons.) 

102. The general object which all laws have, or ought to have, in 
common, is to augment the total happiness of the community; 
and therefore, in the first place, to exclude as far as may be every- 
thing that tends to subtract from that happiness : in other words, 
to exclude mischief. But all punishment is mischief; all punish- 
ment in itself is evil. Upon the principle of utility, if it ought at 
all to be admitted, it ought only to be admitted in as far as it prom- 
ises to exclude some greater evil. (Bentham.) 

103. Experiments for the purpose of ascertaining the functions 
of the various organs in animals cause pain, and as we are not war- 
ranted in causing pain to any sentient creature, such experiments 
are wrong. 

104. Thou shalt not bear false witness against thy neighbour, 

105. It is injustice to the intellect of women to refuse them the 
suffrage ; for the reigns of many queens have been famous for 
literary productions. (Oxford.) 

106. The two propositions, ^Aristotle is dead,' and ^Aristotle is 
living,' are both intelligible propositions; they are both of them true 
or both of them false, because all intelligible propositions must be 
either true or false. (Edinburgh.) 

107. He is innocent, for he has faced his accusers ; a guilty man 
would run away. (Hyslop.) 



Questions and Exercises 445 

^ 108. All civilized people are inhabitants of the temperate zones. 
Few Indians are civilized, and therefore few Indians are inhabitants 
of the temperate zones. (Hyslop.) 

109. In what are called our free actions we are either undeter- 
mined by motives, in which case we act from pure caprice, or we 
are determined by motives, in which case our freedom has no real 
existence. (St. Andrews.) 

1 10. If a nation wants Protection, it is not prosperous under Free 
Trade, as England must be, since it does not want Protection. 
(St. Andrevv^s.) 

111. Either all the facts of the major premise of any syllogism 
have been examined, or some of them have not; therefore the 
syllogism is either useless or fallacious. (St. Andrews.) 

112. Few treatises of science convey important truths without 
intermixture of error, in a perspicuous and interesting form ; and 
therefore, though a treatise would deserve much attention which 
should possess such excellence, it is plain that few treatises of 
science deserve much attention. (Whately.) 

113. All aristocracies are self-willed ; some self-willed people are 
not cruel ; therefore some aristocracies are not cruel. 

114. Some men of inferior ability are legislators. All peers are 
legislators. Therefore some peers are men of inferior ability. 

115. All able men are consistent with themselves; he who 
changes his opinions is not consistent with himself; therefore he 
who changes his opinions is not an able man. 

116. To allow every man an unbounded freedom of speech 
must always be, on the whole, advantageous to the state ; for it is 
highly conducive to the interests of the community that each 
individual should enjoy a liberty perfectly unlimited of express- 
ing his sentiments. (Whately.) 

117. He who necessarily lies or tells the truth is not a free 
agent; but you must necessarily lie or tell the truth; therefore 
you are not a free agent. (Whately.) 



446 Questions and Exercises 

118 It is no uncommon occurrence to gain a high prize in the 
lottery; and what is no uncommon occurrence may reasonably 
be expected; therefore I may reasonably expect to gain a high 
prize on my ticket. (Whately.) 

119. If genius were normal, it would be good and worthy of 
cultivation, but being abnormal, it is not. (St. Andrews.) 

120. If truthfulness is never found save with scrupulousness, 
and if truthfulness is incompatible with stupidity, it follows that 
stupidity and scrupulousness can never be associated. (St. 
Andrews.) 

121. Either the proposition (S is P) is true, or it is not true; and 
since you must either accept it as true or deny it as false, you can- 
not, logically, in any way suspend your judgment in the matter. 
(St. Andrews.) 

122. What is the use of all this teaching? Every day you 
hear of a fraud or forgery, by some one who might have led an inno- 
cent life, if he had never learned to read and write. (Edinburgh.) 

123. Pious men only are fit to be ministers of religion; some 
men who have not received a college education are pious men, 
therefore such men are fitted to be ministers of religion. 

124. What fallacy did Columbus commit when he proved that 
an ^gg could stand on end? (Jevons.) 

125. No traitor is to be trusted, John is no traitor, and there- 
fore is to be trusted. 

126. Against what fallacy does the proverb, ^ All that glitters 
is not gold,' warn us? 

127. Livy describes prodigies in his history, therefore he is 
never to be believed. 

128. The theory of evolution is true, for it is accepted by every 
scientific biologist. 

129. The theory of evolution is not true, for it was not accepted 
by Agassiz, or by Gladstone; moreover, you cannot accept this 
doctrine, for it is disclaimed by the authorities of yqur church. 



Questions and Exercises 447 

130. The advantages which would accrue to the working classes 
are not sufficient to justify Protection, neither are the advantages 
which it would bring to the farmers or the manufacturers, or to 
any other class in the community; Protection, therefore, has not 
enough advantages to justify it. 
^^^. 131. No man should be punished if he is innocent; this man 
should not be punished ; therefore he is innocent. 

132. The student of history is compelled to admit the law of 
progress, for he finds that society has never stood still. 

133. I will not do this act because it is unjust; I know that it is 
unjust because my conscience tells me so, and my conscience tells 
me so because the act is wrong. 

134. Gold and silver are wealth; therefore the diminution of 
the gold and silver of the country by exportation is a diminution 
of the wealth of the country. 

135. Nations are justified in revolting, when badly governed, 
for every people has a right to a good government. (Edinburgh.) 

136. When Croesus was about to make war upon Cyrus, King 
of Persia, he consulted the oracle at Delphi, and received for an 
answer that, if he should wage war against the Persians, he would 
overthrow a mighty empire. 

137. England has a gold coinage, and is a very wealthy country, 
therefore it may be inferred that other countries having a gold 
coinage will be wealthy. 

138. Your arguments against the philosophy of Hegel are of 
no value; for you uphold that of Schopenhauer, which is equally 
repugnant to common sense. 

139. For those who are bent on cultivating their minds by dili- 
gent study, the incitement of academical honours is unnecessary; 
and it is ineffectual for the idle, and such as are indifferent to 
mental improvement; therefore the incitement of academical 
honours is either unnecessary or ineffectual. 



448 Questions and Exercises 

140. Without order there is no living in public society, because 
the want thereof is the mother of confusion, whereupon division 
of necessity followeth ; and out of division, destruction. 

141. If it is always impossible not to sin, it is always unjust to 
punish. Now it is always impossible not to sin, for all that is 
predetermined is necessary, and all that is foreseen is predeter- 
mined, and every event is foreseen. Hence it is always unjust to 
punish. (Leibniz, Theodicy^ 

142. If a gas is heated, its temperature rises; if its temperature 
rises, its elastic force increases; if its elastic force increases, the 
pressure on the walls of the containing vessel increases; there- 
fore if a gas is heated, the pressure on the walls of the containing 
vessel increases. (Ray.) 

143. The end of human life is either perfection or happiness; 
death is the end of human life ; therefore death is either perfection 
or happiness. 

144. Can these three propositions be true together? (i) Only 
mammals produce their young alive. (2) The duck-mole is a 
mammal. (3) Among creatures that lay eggs are duck-moles. 
Assuming (2) and (3) to be true, what conclusion follows ? (St. 
Andrews.) 

145. Theft is a crime; theft was encouraged by the laws of 
Sparta ; therefore the laws of Sparta encouraged crime. (Whately .) 

146. Opium is a'poison; but physicians advise some of their 
patients to take opium; therefore physicians advise some of their 
patients to take poison. (Whately.) 

147. You must believe yourself to be infallible, for you always 
believe the judgment you have formed to be right, and he whose 
judgment is always right, is infallible. (Whately.) 

148. If light consisted of material particles, it would possess 
momentum ; it cannot consist of material particles, for it does not 
possess momentum. 



Questions and Exercises 449 

149. This person is very learned, and very sociable, hence it fol- 
lows that learning increases sociability. 

150. Why advocate socialism? Until men become morally 
perfect, it is impossible; when they have become so, it will be 
unnecessary. (Edinburgh.) In what ways could you reply to 
this? 

151. The diameter of the earth is, in round numbers, forty 
millions of feet. Consequently the attraction of a sphere of the 
same mean density as the earth, but one foot in diameter, will be 
TOQ-roo" "oo" P^^t ^^ attraction of the earth ; that is, 4-00T-00T0 ^^ 
the weight of the body attracted. Consequently, if we should 
measure the attraction of such a sphere of lead, and find that 
it was just 4-o-oo-o"oo~o ^^^^ ^^ ^^^ weight of the body attracted, 
we would conclude that the mean density of the earth was equal 
to that of lead. But the attraction is actually found to be nearly 
twice as great as this; consequently a leaden sphere is nearly 
twice as dense as the average of the matter composing the earth. 
(Newcomb, Popular Astronomy.) 

152. Mr. C. said that he was certain that the donors gave the 
property to the institution with a distinct and unanimous under- 
standing as to its future use. The directors who acted for the 
institution in this transfer must necessarily have had an under- 
standing, either the same as that of the donors, or different. If the 
understanding of the directors was the same as that of the donors, 
then they, the former, were unquestionably bound to live up to 
that understanding. If it was different, then the property was 
conveyed on a misunderstanding, and every dictate of honour 
and fair play would demand the return of the property. 

153. There is no connection between sex and the ballot. If 
woman is like man, and it is right for man to vote, it must be 
right for woman to do so. If woman is unlike man, he can never 
truly represent her, and she ought to be allowed to represent herself. 
(From letter to N,Y, Times.) 

2 G 



450 Questions and Exercises 

154. The British people are fed from abroad. Not only does 
the teeming industry on which the prosperity of the people rests 
derive its necessary materials from other countries, but the food 
raised on the islands is wholly insufficient to the daily require- 
ments of the people. Without imports of food they would in a 
measurable period be sorely distressed, and ultimately would 
face something very like famine. It is on the navy, therefore, that 
their very life depends. 

155. When dealing with such bodies as the sun, moon, or stars, 
the force of gravitation overpowers all other forces, and all electric 
and magnetic attractions sink by comparison into insignificance. 
These tremendous forces must be transmitted by the ether, for there 
is undoubtedly a connecting link of some kind. There can be no 
attraction across really empty space. 

156. '^ The fundamental medium filling all space, if there be such, 
must be ultimately incompressible, otherwise it would be composed 
of parts, and we should have to seek for something still more 
fundamental to fill the interstices. '' (Sir Oliver Lodge.) 

157. Only those messages which have been prepaid will be 
delivered. This message has been prepaid, and therefore it will be 
delivered. 

158. The right to use and kill animals for the relief and con- 
venience of man is universally recognized throughout Christen- 
dom and, in general, throughout the civilized world. Dominion 
over the animate creation means, of course, the right of man 
to use animals for his own good ; and those who kill animals for 
food have a poor logical ground to stand on when they object to 
the use of animals for the experimentation in scientific laboratories 
by experts who are aiming to discover remedies for the terrible 
diseases which attack and destroy human life. Shall a man have 
animals killed for his nourishment and pleasure, and object to 
that experimental research upon animals which has enabled 
scientific and medical investigators to conquer numerous diseases ? 



Questions and Exercises 45 1 

159. It is not surprising that Senators X. and Y., though pro- 
nounced protectionists, should earnestly support the repeal of the 
duty on hides. Not only are the interests of their immediate con- 
stituents, the tanners and leather goods m.anuf acturers of their State, 
enlisted in favour of this measure, but the measure is in reality one 
of sound protection, the only kind, in fact, which any industry in 
the United States can reasonably ask for. Certainly there is no 
way of aiding a manufacturer to meet competition more effectual or 
more just than to release his materials from an arbitrary tax. 

160. The forces of gravitation, electricity, etc., are in constant 
action between the material bodies which make up the universe. 
But we are convinced that there can be no ^ action at a distance,' 
that is, across empty space. We are therefore confident that a 
physical medium exists, which we call ether, and which fills out 
the space between the parts of grosser matter, and serves as the 
medium of all these forces. 

But when we come to consider the nature of this medium, we 
see that to serve this function it must have certain very strange 
qualities, not to be found elsewhere, such as perfect continuity, 
absolute incompressibiiity, indefinite elasticity. Further, it is 
impalpable and invisible, inaccessible to our most delicate instru- 
ments. Is it not, then, a wonderful and mysterious agent ? And 
may we not assent to the words of Sir Oliver Lodge, who says 
that when we once know its secrets : — 

^'I feel as if it would be no merely material prospect that will be 
opening on our view, but some glimpse into a region of the universe 
which science has never entered yet, but which has been sought 
from far, and perhaps blindly apprehended by painter and poet, 
by philosopher and saint." 

161. If pain is long continued, it is not severe ; and if it is severe, 
it does not last long. (Stoic axiom.) 

162. ''We are not inclined to ascribe much logical value to 
that analysis of the inductive method which Bacon has given. It 



452 Questions and Exercises 

is indeed an elaborate and correct analysis. But it is an analysis 
of that which we are all doing from morning to night, and which 
we continue to do even in our dreams." (Macaulay, Essay on 
Bacon.) 

163. It has been pointed out by Cohen that reasoning to the 
following effect occurs in some works on mathematics : '^ A magni- 
tude required for the solution of a problem must satisfy a partic- 
ular equation, and as the magnitude x satisfies this equation, it 
is therefore the magnitude required." Examine the logical valid- 
ity of this argument. (Jevons.) 

164. ^^To condemn coalitions in the abstract is manifestly 
absurd; since, in a popular government, no good can be done 
without concert, and no concert can be obtained without compro- 
mise. . . . But most peculiarly inconsistent and unreasonable 
is the conduct of those who, while they profess strong party feel- 
ings, yet entertain a superstitious aversion to coalitions. Every 
argument which can be urged against coalitions, as such, is also 
an argument against party connections. Every argument by 
which party connections can be defended is a defence of coalitions. 
What coalitions are to parties, parties are to individuals. The 
members of a party, in order to promote some great common object, 
agree to waive all subordinate differences. Men are not thought 
unprincipled for acting thus; because it is evident that without 
such mutual self-sacrifices of individual opinion, no government 
can be formed. . . . We must extend the same indulgence to a 
coalition between parties. If they agree on every important prac- 
tical question ... no party man can, on his own principles, blame 
them for uniting." (Macaulay.) 

165. The bill imposing a 2 per cent tax upon the net earnings 
of corporations is one of those hybrids abhorred by nature and 
disliked by man. It has a double purpose, the bringing of revenue 
into the Treasury and the securing of Federal control over corpo- 
rations. The two purposes are dissimilar, unrelated, and, if not 



Questions and Exercises 453 

incompatible, are at least so far from kin that the gross impro- 
priety of attempting to bring them together in a statute is obvious. 
There is no principle of economics, no just principle or theory 
of taxation, that warrants the singling out of incorporated business 
interests from the whole mass of business interests as the subject 
of this exaction. Partnerships and individual concerns enjoy the 
same protection of the laws, the same benefits of orderly Govern- 
ment, that accrue to corporations. (N .Y . Times) 

166. The removal of a tyrant by assassination might at times 
bring relief to a whole nation, but we should not for that reason 
consider ourselves justified in setting apart a class of men specially 
licensed to remove objectionable rulers, as we license our vivi- 
sectors to do what it is illegal for any one else to do. The carman, 
or small tradesman, who is punished — quite rightly — for over- 
working his horse, does not do it for the mere pleasure of being 
cruel. He m.ay have a family to support, and must get all he can 
out of the animal, regardless of his feelings. In what respect is 
the vivisectors' cruelty different from his, morally? If utility, 
consisting in diminished pain or increased pleasure, carries moral 
right with it, then almost all cruelty may be defended. (Letter 
to Saturday Review!) 

167. " No, neither the uneducated judgment nor the instincts of 
the uneducated can ever come to have more than the very slightest 
value in the determination of what is true or false in art. A genuine 
democracy of social condition may or may not be practically pos- 
sible; but the democracy of intellect, happily, is impossible. . . . 
In material matters, even, in matters most within his reach, has the 
labourer ever been able to understand a machine, which he will 
come in time to prize for its service, until it has been laboriously 
explained to him, and, for the most part, forced upon him for 
his good ? How, then, is he to understand a poem, which must 
always continue to seem to him a useless thing, useless at all events 
to him ? " (Symons.) 



454 Questions and Exercises 

i68. ^'The fashionable logic of the Greeks was far from strict. 
Logic never can be strict where books are scarce, and where 
information is conveyed orally. We are all aware how frequently 
fallacies which, when set down on paper, are at once detected, pass 
for unanswerable arguments when dexterously and volubly urged 
in Parliament or in private conversation. The reason is evident. 
We cannot inspect them closely enough to perceive their inaccuracy. 
We cannot readily compare them with each other. . . . Almost 
all the education of a Greek consisted in talking and listening." 
(Macaulay.) 

169. [The ^'Peculiar People" have got themselves into trouble 
again. A coroner's jury has returned a verdict of manslaughter 
against two parents who were prevented by religious scruples from 
obtaining medical assistance for their child.] . . . But it is 
advisable for the State to interfere with a course of procedure that 
promises to remove one of the gravest dangers of modern civilization. 
Anything which tends to check over-population should recommend 
itself to the careful consideration of political economists. And the 
methods of the ^^ Peculiar People" are, after all, nothing more than 
a practical application of the law of evolution. It is only the fittest 
who are allowed to survive, the weaklings are left to die ; and it is 
possible that this sect, unless interfered with, will provide us with a 
new and sturdy race of men and women. It may be found more 
expedient to encourage the ^'Peculiar People" than to nip in the 
bud one of the most promising remedies ever offered to suffering 
humanity. (Saturday Review^ 

170. In ^^Is Shakespeare Dead?" Mark Twain argues that 
Shakespeare was either a lawyer or not the author of the works 
which go under his name. To the student of Shakespeare this must 
appear (with all due respect to the learned Mr. Twain) silly. Might 
he not, with equal reason, claim that Shakespeare must have been 
a doctor, a warrior, a priest, a king, a fool, a woman, or any other 
of the many types of beings he so marvellously created, or else inca- 



Questions and Exercises 455 

pable of producing such works ? In this instance, it appears to me, 
Mark Twain has o'erleaped himself and fallen on the wrong side. 
(Letter to A^.F. riw^.) 

171. If the Bible is an inspired book, it ought to be true. . . . 
If the Bible is true, slavery is right, and the world should go back 
to the barbarism of lash and chain. If the Bible is true, polygamy 
is the highest form of virtue. ... If the Bible is true, the science 
known as astronomy is a collection of mistakes. ... If the 
Bible is true, the science known as geology is false and every fossil 
is a petrified perjurer. 

The defenders of orthodox creeds should have the courage to 
candidly answer at least two questions: First, Is the Bible 
inspired? Second, Is the Bible true? And when they answer 
these questions, they should remember that if the Bible is true, it 
needs no inspiration, and that if not true, inspiration can do it no 
good. (R. G. Ingersoll.) 

172. Let it be possible that universal peace can be enforced. 
The result would be to petrify the present status quo, both territorial 
and dynastic, unless the prodigious task of revising it were under- 
taken as a preliminary, in which case peace might be regarded 
as adjourned sine die. As for the present status quo, there are 
few people indeed who would welcome its permanence. {Saturday 
Review.) 

173. If the principle be once admitted and established that the 
Federal Government may lay a tax upon a corporation doing busi- 
ness under a State charter, there can be no limitation. In Mc- 
culloch vs. Maryland, Chief Justice Marshall laid down the 
memorable principle that ^'the power to tax involves the power to 
destroy," and ''the power to destroy may defeat and render useless 
the power to create." If Congress may pass a law levying a tax of 
2 per cent upon corporations created by a State, many of them 
doing business exclusively within the State, then it may under the 
principle enunciated by Marshall impose a tax of 50 or 100 per 



456 Qtiestions and Exercises 

cent upon the income of such corporations. It may destroy 
them altogether, and that means that the enactment of this tax 
bill sets up the principle that the Federal Government may com- 
pletely annul the right of a State to create corporations and au- 
thorize them to do business, a right not derived from the Federal 
Government, but possessed by the sovereign States before the 
Federal Government was created. {N Y . Times.) 

174. Nevertheless, impertinence or not, pedagogy ought to be 
able to show, if its theory be true, that the faculties of those trained 
in the formal school exercises can be successfully applied to the 
various world problems. But by this test the folly of the educa- 
tional theory becomes manifest. If algebraic exercises train the 
ability merely to solve algebraic problems of the same character as 
those used in school, and do not train the pupils in the problems 
of commerce, government, society, morals, etc., the subject is then 
manifestly worthless to the world, because the world does not 
use school algebra. If Latin trains the faculty of discriminating 
differences only in Latin, and not in world problems, then it is con- 
fessedly useless, because Latin genders are not used by the world. 
(F. Burk.) 

175. As to Mr. Balfour's argument that legislation against im- 
morality can only be of use when there is already some germ of 
moral disapproval against the practice aimed at, it is very likely 
true. But this does not touch the clauses against smoking by 
children. There is a very general feeling of disapproval of chil- 
dren smoking, and it is a moral disapproval. We see for our- 
selves, and physicians produce much evidence to show, that smok- 
ing by children causes mental and physical disease, and therefore 
what even conventionally we agree to call strictly moral deteriora- 
tion. ... If legislation has this germ to work on for repressing 
juvenile smoking, there is as good a priori argument for it as in 
any other instance where legislation is applied to expand the germ 
into a fully developed moral rule of the community, recognized by 



Questions and Exercises 457 

law. We do not leave the germs to take care of themselves; we 
foster them; and morality is more easily accepted as morality 
when there is a law at the back of it. Most people like to be on 
the side of the lavv^; it is more respectable. . . . In theory it is 
very difficult to say when the morality of some should be imposed 
on others ; but this is what law generally comes to. It is a moral 
feeling which gives rise to the health laws; and we impose them 
on many who think they ought to do as they like either in ignorance 
or self-will. . . . But the essential character of a law is that it is 
compulsory. It is no use passing it unless we are prepared to apply 
compulsion at all necessary points. {Saturday Review.) 

176. If adopted just to avoid the appearance of charity, the Car- 
negie foundation's plan to pension college teachers without regard to 
their private means seems hardly necessary. Only a few hyper- 
sensitive souls insist upon viewing the endowment as a poor fund. 
Everybody else perceives that there is no difference whatever 
between money given to a college for a chair in physics, and money 
given for a retiring allowance to a professor of physics. The man 
who accepts as salary the interest on the first sum is just as much 
and just as little an object of charity as the pensioner. The 
latter has infinitely less cause for humiliation than the well-to-do 
lawyer who secures $5000 worth of education for his son at a cost 
of $600 in tuition fees. The college professor has earned his pen- 
sion by hard work ; it is only deferred salary. If he cannot accept 
it as such, consistency will force him to resign at once; for all his 
academic earnings are equally tainted with benevolence." {Na- 
tion.) 

177. ^' A asserts with incorrigible optimism that ^without too 
much you cannot have enough of anything. Lots of inferior books, 
lots of bad statues, lots of dull speeches, of tenth-rate men and 
women, as a condition of the few precious specimens in either 
kind being reahzed.' As the condition, yes; but as the cause, no. 
We can never have the precious things in literature merely by add- 
ing to the multitude of cheap things." {Nation,) 



458 Questions and Exercises 

What fallacy does this passage point out? 

178. It is difficult to deal with the * militant suffragettes.' 
One knows this difficulty in private life. Nothing is more 
awkward than to be assaulted by a woman. Equally difficult 
is the position for a man whom a lady has insulted. He has 
no remedy. This very thought, that chivalry forbids a man to 
retaliate, and in many circumstances even to defend himself, will 
usually make a lady especially careful not to insult a man. It is 
the woman's side of chivalry. But chivalry is surely for men to 
practise and women to accept. Put '^profit by '' for ^' accept," and 
you get precisely the suffragette view of the matter. As fellow- 
men they claim the right to use violence; as women, they claim 
the right to chivalry. A moment's thought of the position in which 
they put the police, for instance, — mere agents who have no option 
but to do what they are told, — shows these women's tactics to be 
mean. 

It is in vain to show them how they are obstructing their own 
cause. Force may be a very good way to attain your object, if 
you can get force enough ; if you cannot, it is the worst possible way. 
It may always be reasonable for men to resort to force ; they may 
any time be able to compel where they cannot persuade. But for 
women it must always be idle. No multitudes of suffragettes will 
ever terrorize, not to speak of compelling, anybody to do anything. 
There is nothing impressive in the sight of a few excited women 
hustling the police, or being hustled by them. The suffragette 
leaders boast that their campaign of disorder has sent up the 
numbers of their organization by leaps and bounds, but this is 
no evidence of public conversion to votes for women. Make 
yourself notorious, and you will always get imitators and admirers. 
Featherheads are always drawn to public names that figure in 
police courts. {Saturday Review.) 

179. ^^If young collegians from eighteen to twenty-two do not 
find in college a chance for a serious, unbiassed scrutiny of letters 



Questions and Exercises 459 

or philosophy or history or science, in nine cases out of ten they will 
never again get the opportunity ; and, so far as the real purpose of 
university life is concerned, they might better waste their time and 
their father's money at home. Bitter experience of the present 
generation of college life goes far to justify what we were rashly 
inclined to regard as the amiable or picturesque crotchets of early 
educators. It was not without a substantial reason that colleges 
originally took on the semi-monastic mode of life, with a common 
garb, a common meal, and a communal life. It segregated the 
scholar from the world during his scholastic apprenticeship, and 
reduced distinctions to a minimum within the cloister. It may 
seem a far call from the mediaeval college to our military academy 
at West Point, but the scheme of social organization is not dis- 
similar. The uniform donned at entrance amalgamates into a 
common body the farmer's son and the financier's heir. The mess 
table and the barracks life do not reduce the cadets to a dead level, 
but make for the emergence of real, not fictitious, merit. The 
unquestioned eSiciency of West Point as an educational machine 
is in large part traceable to a modern adherence to tried educa- 
tional methods of the past, and to an enforced exclusion of 
parasitic interests that infest our colleges and universities." 
(Nation^! 

180. ^' (The constitution) has made treaties part of our municipal 
law ; but it has not assigned to them any particular degree of author- 
ity, nor declared that laws so enacted shall be irrepealable. No 
supremacy is assigned to treaties over acts of Congress. That they 
are not perpetual, and must be in some way repealable, all will 
agree. If the president and the senate alone possess the power 
to repeal or abrogate the law found in a treaty, inasmuch as they 
can change or abrogate one treaty only by making another incon- 
sistent with the first, the government of the United States could not 
act at all to that effect without the consent of some foreign govern- 
ment. I do not consider — I am not aware that it "^has ever been 



460 Questions and Exercises 

considered — that the constitution has placed our country in this 
helpless condition. ... If, therefore, it were admitted that the 
treaty between the United States and France did contain an express 
stipulation that the United States would not exclude slavery from 
(the Louisiana Purchase), the Supreme Court could not declare 
that an act of Congress excluding it was void by reason of the 
treaty." (B. R. Curtis.) 

181. ^^Our ideas reach no farther than our experience. We 
have no experience of divine attributes and operations. I need not 
conclude my syllogism. You can draw the inference yourself." 
(Hume.) 

182. '^ No one would be so foolish as to argue that English has not 
profited by these communions with the other great literatures of 
the world. On the intellectual side the profit is incalculably great. 
Abundance, richness, flexibility, tolerance, colour, range, are all cos- 
mopolitan qualities which, in great measure, English literature pos- 
sesses. Yet to have all these without national virtues profiteth 
nothing; and it is only when a literature begins to lay aside its 
national virtues and becomes to a certain extent unmoral, or even 
immoral, that it enters triumphantly upon the conquest of the 
world. ... It almost seems that the qualities which make for 
the federation of the world are not the national virtues, but the 
international vices. ... A world-language has terrible things to 
express. If English does not wish to become a vessel of wrath, it 
had better not dwell too long on its imperialistic dreams. It had 
better come home and fight for its altars and its fires, and revive 
its healthy loves and hates. . . . Cosmopolitanism is a dear 
teacher, and the pith of its lesson is only this : A man cannot be 
all things to all men and be much of a man himself." {Nation.) 

183. Are we justified in saying that the Catholic Church is of 
divine origin because the Pagans failed to destroy it' by persecu- 
tion? 

We will put the Cardinal's statement in form: — 



Questions and Exercises 461 

Paganism failed to destroy Catholicism by persecution; therefore 
Catholicism is of divine origin. Let us make an application of 
this logic. Catholicism failed to destroy Protestantism by perse- 
cution; therefore Protestantism is of divine origin. Catholicism 
and Protestantism united failed to destroy Infidelity; therefore 
Infidelity is of divine origin. Let us make another application. 
Paganism did not succeed in destroying Catholicism; therefore 
Paganism was a false religion. Catholicism did not succeed in 
destroying Protestantism; therefore Catholicism is a false religion. 
Catholicism and Protestantism combined failed to destroy Infi- 
delity; therefore both Catholicism and Protestantism are false 
religions. (Reply of R. G. Ingersoll to Cardinal Manning.) 

184. Nothing is demonstrable, unless the contrary implies a 
contradiction. Nothing that is distinctly conceivable implies a 
contradiction. Whatever v/e conceive as existent, we can also 
conceive as non-existent. There is no being, therefore, whose 
non-existence implies a. contradiction. Consequently, there is 
no being whose existence is demonstrable. (Hume.) 

185. ^' The purpose (of war) is to be secured by a coercion of the 
power against which you act. The customs and opinions of mod- 
ern civilization have recognized certain modes of coercing the 
power you are acting against as justifiable. Injury to private 
persons or their property is avoided as far as it reasonably can be 
done. Wherever private property is taken or destroyed, it is be- 
cause it is of such a character, or so situated, as to make its capture 
a justifiable means of coercing the power with which you are at 
war. . . . But the humanity of modern times has abstained 
from the taking of private property not liable to use in war, when 
on land. Some of the reasons for this are the infinite varieties of 
its character, the difficulty of discriminating among these varieties, 
the need of much of it to support the life of non-combatant persons 
and animals, and, above all, the moral dangers attending searches 
and captures in households. But on the high seas these reasons 



462 Questions and Exercises 

do not apply. Strictly personal effects are not taken. Merchan- 
dise sent to sea is sent voluntarily embarked by merchants on an 
enterprise of profit, taking the risk in the custody of men trained 
and paid for the business, and its value is usually capable of com- 
pensation in money." (R. H. Dana.) 

186. ^^ The literature which makes aesthetic gratification the end 
of existence defeats its own end. Pursued as an ultimate goal, 
it leads sooner or later into quagmires. The aesthete wanders 
from home in the quest of new and strange beauties. His truant 
feet stray from . . . the sound to the unsound, and thence to the 
insane; from the chaste to the unchaste, and thence to the inde- 
cent. Yet the price of illicit aesthetic pleasure is the loss of all 
aesthetic pleasure. The unhappy man, as M. Lecomte says, 
who little by little allows himself to be soiled with all that filth, 
becomes finally insensible to a vigorous thought, an expressive 
portrait, or the proud wing of poetry." {Nation.) 

187. "" The attorney-general tells us that all persons whom he and 
his associates choose to denounce for giving aid to the rebellion are 
to be treated as being themselves a part of the rebellion — they are 
public enemies, and therefore they may be punished without being 
found guilty by a competent court or jury. This convenient 
rule would outlaw every citizen the moment he is charged 
with a political offence. But political offenders are precisely 
the class of persons who most need the protection of a court 
and jury, for the prosecutions against them are most likely 
to be unfounded both in fact and in law. Whether innocent 
or guilty, to accuse is to convict them before the ignorant 
and bigoted men who generally sit in military courts. But 
this court decided in the Prize Cases that all who live in the 
enemy's territory are public enemies, without regard to their per- 
sonal sentiments or conduct ; and the converse of the statement is 
equally true, — that all who reside inside of our own territory are 
to be treated as under the protection of the law. If they help the 



Questions and Exercises 463 

enemy, they are criminals ; but they cannot be punished without 
legal conviction." (Jeremiah S. Black.) 

Analyze the above passage carefully. 

Is what Justice Black calls ^the converse of the statement' its 
logical converse? And, if not, can it be derived from the first 
statement by any of the processes of ^ immediate inference ' ? 

188. We should limit public expenditures to public purposes. 
Take as little as possible out of the pocket of the tax-payer, and 
use what is taken only for the purposes which can be justified 
on public grounds. What will happen if you go on the 
contrary principle — a principle which the Socialists adopt 
and which some semi-Socialists sympathize with — the prin- 
ciple that it is just to use taxation as a means of equalizing the 
inequalities of fortune ? Surely if that principle obtains, the people 
will learn that their prosperity is to be secured, not by their own 
industrial efforts, but by their political exertions ; politics will be- 
come a game of grab if you once admit that the State is justified in 
taking from A for the private benefit of B . There is no end to the 
demands that may then be made, except this, that the State will 
be ruined because everybody, instead of working for himself, will 
be seeing how much he can steal from the State. (Quoted by 
N . Y. Times,) 

189. Mr. X. was as impertinent as he was arrogant in taunting 
his Republican opponents with wishing to form a new party. He 
assumes that anybody who will not accept his interpretation of 
the tariff policy of the party to which he professes to belong is 
disloyal. He chooses to forget that the men who hold to his inter- 
pretation were badly beaten at the last National Convention, and 
that the Senators who are opposing him are faithfully trying to 
carry out the specific pledges of the party made at that convention. 
If they are to be denounced, an entirely new system of party dis- 
cipline and obligation must be devised under which fidelity is 
punished as betrayal, and treachery is rewarded with undisputed 



464 Questions and Exercises 

power. By that system Mr. Taf t,if he remains as true to the Repub- 
lican pledges in action as he has so far in profession, must be read 
out of his party. This is the practical outcome of the position. 
From the standpoint of party expediency it is as risky as from 
the point of view of principle it is immoral. {N . Y. Times.) 

190. If the average mental development reached by the Greeks 
was . . . notonly in excess of that of those modern European races 
whose civilization is reaching such an ascendency in the world to-day, 
but ... as far above it as the mental ability of these latter is above 
that of some of the lowest of the peoples whom they have displaced 
through the operation of natural selection, then it seems extremely 
difficult to reconcile this fact with an unshaken belief in any theory 
according to which intellectual development must be taken as the 
dominant factor in human evolution. We may be prepared to 
accept Sir Henry Maine's view that in an intellectual sense nothing 
moves in this Western world that is not Greek in its origin ; but no 
homage of this kind to the Greek intellect, however well it may be 
deserved, can blind our eyes to the fact that the Greek peoples 
themselves, like the ancient Romans, have absolutely disappeared in 
the human struggle for existence. Even their blood cannot be dis- 
tinguished in the populations of large tracts of Eastern and Southern 
Europe, and Western Asia, where these ruling races were once 
predominant in numbers and influence. (Benjamin Kidd.) 



PART II. — Inductive Methods 

Chapter XIII. — The Problem of Induction 

1 . Explain why syllogistic logic is not a complete account of the 
nature of thinking. 

2. Give a statement of the general problem of Induction. Why 
is there any problem in the case? 

3. Explain the distinction between Induction by Enumeration, 
and Induction by Analysis. 



Questions and Exercises 465 

4. Explain the following terms : Induction by Simple Enumera- 
tion, Prerogative Instances, and Crucial Experiments. 

5. What rules may be given for the selection of instances in an 
inductive investigation? 

6. It is sometimes said that Elimination is the essential principle 
of Induction. Discuss this statement. 

7. Explain the function of Analogy and Hypotheses in Induc- 
tion. 

Chapter XIV 

1. What is the general assumption of all Inductive thinking? 
Explain the relation of this assumption to the laws of Thought. 

2. What is meant by a category of Thought ? Illustrate. What 
is the distinction between a ' dynamic ' and a ' static ' category? 

3. What is to be said regarding the division of Inductive meth- 
ods into methods of Observation, and methods of Explanation? 
Would it be permissible to add Experimental methods as a third 
and independent class? 

4. Explain the relation between facts and theories. 

5. What is the distinction between 'empiricaP and ^scientific' 
knowledge ? 

Chapter XV. — Enumeration and Statistics 

1. What is the justification for beginning our account of the 
inductive methods with Enumeration? 

2. Explain how it is sometimes possible to reach certain con- 
clusions on the basis of instances. In what respect are such con- 
clusions defective? 

3. For what purpose are Statistics employed? To what classes 
of phenomena are they applied? Explain the statement that 
Statistics are valuable only when compiled intelligently. 

4. State and distinguish three uses to which Statistics may be 
put. 

2H 



466 Questions and Exercises 

5. Explain how Statistics may suggest causal laws, or confirm 
our expectation of them. May Statistics also be used to disprove 
a proposed law of causal connection? Illustrate your answer. 

6. Explain what is meant by the ^average/ the ^mean/ and the 
* mode,' and show how each is obtained. 

7. How does the procedure of insurance companies differ from 
gambling? 

Chapter XVI. — Causal Determination 

1. What are the two main principles upon which the canons 
proposed by Mill are founded? 

2. Give the canon of the method of Agreement, and illustrate 
its use. 

3. ^I have noticed that A always precedes B ; it is therefore the 
cause of B.' Is this good reasoning? 

4. What is meant by the ^Plurality of Causes' and by the 
^Reciprocity of Causes'? 

5. Under what disadvantages does the method of Agreement 
labour? How is it supplemented? 

6. State and illustrate the canon of the method of Difference. 

7. Why is this method applicable only to the spheres where 
experiment can be employed? Would it be safe to depend upon 
this method in determining the causes of social or political con- 
ditions ? 

8. How might the canons of Agreement and Difference re- 
spectively be stated negatively, as principles of Elimination? 
Would this statement do full justice to the inductive procedure 
involved ? 

Chapter XVII. — Causal Determination {continued) 

1. Where do we employ the Joint method? 

2. What precisely would it be necessary to establish in order to 
establish inductively that some change in the tariff laws was bene- 
ficial to the country ? 



Questions and Exercises 467 

3. Explain what qualifications it is necessary to introduce in 
interpreting Mill's statement of the Joint method. 

4. 'One of the main characteristics of modern science is its 
quantitative nature.' Explain. 

5. How does the law of Concomitant Variations assist us in 
determining causal relations? 

6. In what two ways may the method of Residues be applied? 

7. Mention some discoveries to which the investigation of un- 
explained residues has led. 

Chapter XVIII. — Analogy 

1. Why do we include Analogy among the methods of Ex- 
planation ? 

2. What do you mean by Analogy ? What is the principle upon 
which it proceeds ? 

3. How is the word used in mathematical reasoning, and in 
physiology ? 

4. Into what Figure of the Syllogism does an argument from 
Analogy naturally fall? Is the argument formally valid, and if 
not, to what syllogistic fallacy does it correspond? 

5. Explain how Analogy may suggest a true law or explanatory 
principle. 

6. Why do we speak of Analogy as Incomplete Explanation? 

7. If all analogical reasoning yields only probability, is not one 
analogy as good as another for purposes of inference? If not, 
upon what does the value of an inference from Analogy depend? 

Chapter XIX. — The Use of Hypotheses 

1. How do you distinguish the terms 'theory' and 'hypothesis'? 

2. What is an hypothesis, and how is it used? 

3. Do hypotheses play any part in assisting Observation? 
Explain and illustrate. 

4. Give some instances in which hypotheses have proved in- 
jurious, and have misled people regarding the nature of facts. 



468 Questions and Exercises 

5. ^Hypotheses are formed by the imagination working in 
dependence upon facts and guided by analogy.' Explain. 

6. What are the steps in the proof of an hypothesis? 

7. Explain what part is played by Induction and Deduction 
respectively in using hypotheses. 

8. What part dees Elimination play in the proof of an hypothe- 
sis? Explain the nature of the formal fallacy involved in the 
statement that an hypothesis is established when its results are 
shown to be true. How is this difficulty overcome ? 

9. What canons have been laid down to which a good hy- 
pothesis must conform? Why are the first and third of these 
rules of little value ? 

10. Explain why an unverifiable hypothesis is not worth dis- 
cussing. 

Chapter XX. — Fallacies of Induction 

1. What is the source of fallacy? How far is it true that the 
study of Logic can protect us from fallacies ? 

2. How do you classify Inductive Fallacies? 

3. Explain and illustrate the following fallacies: Question- 
begging Epithet, Equivocation, Fallacies due to Figurative Lan- 
guage, 

4. Explain and illustrate the tendency of the mind to neglect 
negative cases. 

5. Is it an easy matter to ^tell just what we saw and heard' at a 
particular time? 

6. What do you mean by post hoc ergo propter hoc ? Why may 
we take this as the general type of inductive fallacies ? 

7. What did Bacon mean by the Idols of the Cave, of the 
Tribe, of the Market-Place, of the Theatre? 

8. ^ Every age, as well as every individual, has its idols.' Ex- 
plain this statement. 



Questions and Exercises 469 

Miscellaneous Examples of Inductive Arguments 

Analyze the examples of inductive reasoning given below, and 
point out what methods are employed, indicating also whether or 
not the conclusion is completely established, and naming the 
fallacy, if any be present : — 

1. In my experience A has been invariably preceded by B, and 
we may therefore conclude that^B is the cause of A. 

2. Scarlet poppies, scarlet verbenas, the scarlet hawthorn, and 
honeysuckle are all odourless, therefore we may conclude that all 
scarlet flowers are destitute of odour. 

3. What inference, if any, can be drawn from the following 
statement: ^In nine counties, in which the population is from 100 
to 150 per square mile, the births are 296 to 100 marriages; in 
sixteen counties, with a population of 150 to 200 per square mile, 
the births are 308 to 100 marriages'? 

4. The great famine in Ireland began in 1845 and reached its 
climax in 1848. During this time agrarian crime increased very 
rapidly, until, in 1848, it was more than three times as great as in 
1845. After this time it decreased with the return of better crops, 
until, in 1851, it was only 50 per cent more than it was in 1845. 
It is evident from this that a close relation of cause and effect exists 
between famine and agrarian crime. (Hyslop.) 

5. Sachs maintained, in 1862, that starch is formed by the 
decomposition in chlorophyl of carbon-dioxide gas under the 
influence of light. He found that when all other conditions were 
constant, and light was excluded from a plant, no starch was 
formed ; the single circumstance of readmitting light was accom- 
panied by renewed formation of starch. Further, he found that if 
certain portions of the leaves of an illuminated plant were covered 
with black paper, no starch was found in these portions. 

6. Jupiter gives out more light than it receives from the sun. 
What is the obvious conclusion, and by what method is it reached ? 



4/0 Questions and Exercises 

7. What methods would you employ in order to test the truth 
of the proposition, omne vivum ex vivo ? 

8. It is evident that the green colour of plants holds some neces- 
sary relation to light, for the leaves of plants growing in the dark, 
as potatoes sprouting in a cellar, do not develop this colour. Even 
when leaves have developed the green colour, they lose it if deprived 
of light, as is shown by the process of blanching celery and by the 
effect on the colour if a board has lain upon it for a long time. 
(Coulter.) 

9. Another indication that the green colour is connected with 
light may be obtained from the fact that it is found only in the sur- 
face region of plants. If one cuts across a living twig or into a 
cactus body, the green colour will be seen only in the outer part of 
the section. (Coulter.) 

10. If an active leaf or water plant be submerged in v^^ater in 
a glass vessel and exposed to the light bubbles may be seen com- 
ing from the leaf surface and rising through the water. The 
water is merely a device by which the bubbles of gas may be 
seen. If the leaf is very active, the bubbles are numerous. 
That this activity holds a definite relation to light may be proved 
by gradually removing the vessel containing the leaf from the 
light. As the light diminishes the bubbles diminish in number, 
and when a certain amount of darkness has been reached the 
bubbles will cease entirely. If now the vessel be brought back 
gradually into the light, the bubbles will reappear, more and 
more numerous as the light increases. (Coulter.) 

11. War is a blessing, not an evil. Show me a nation that has 
ever become great without bloodletting. 

12. If wages depend upon the ratio between the amount of 
labour-seeking employment, and the amount of capital devoted to 
its employment, the relative scarcity or abundance of one factor 
must mean the relative abundance or scarcity of the other. Thus 
capital must be relatively abundant where wages are high, and 



Questions and Exercises 471 

relatively scarce where wages are low. Now, as the capital used 
in paying wages must largely consist of the capital-seeking invest- 
ment, the current rate of interest must be the measure of its rela- 
tive abundance or scarcity. So if it be true that wages depend 
upon the ratio between the amount of labour-seeking employment, 
and the capital devoted to its employment, then high wages must 
be accompanied by low interest, and, reversely, low wages must be 
accompanied by high interest. This is not the fact but the con- 
trary. (George.) 

13. Construct an inductive argument to prove that some article 
of food, or some habit, is beneficial or injurious to you, and analyze 
your reasoning, showing the methods which you have employed. 

14. Some comets have been observed to have the same orbits 
as certain meteoric showers. The hypothesis is suggested that all 
meteoric showers may represent the debris of disintegrated comets. 
Biela's comet having been missing for some time, it was accord- 
ingly predicted that when next due it would be replaced by a*mete- 
oric shower. This prediction was verified by observation. 

15. Tyndall found that of twenty-seven sterilized flasks con- 
taining infusion of organic matter, and opened in pure Alpine air, 
not one showed putrefaction ; while of twenty-three similar flasks, 
opened in a hayloft, only two remained free from putrefaction 
after three days. He concluded that putrefaction is due to float- 
ing particles in the air. 

16. The census of 1890 regards immigration as the sufficient 
explanation of the excess of males over females in the population 
of the United States. The results of the same census yield the 
following figures : The excess of white native males, both parents 
native, was 587,458. That of white native males, one or both 
parents foreign-born, was 59,467. Coloured native females were in 
excess of males by 18,128. Foreign-born white males exceeded 
females by 781,429, and foreign-born coloured males were in excess 
by 102,864. What is the bearing of these figures upon the explana- 



4/2 Questions and Exetcises 

tion given by the census, and do they confirm or disprove it? 
(Willcox.) 

17. Regarding our social systems as organic growths, there 
appears to be a close analogy between their life-history and that 
of organic forms in general. We have, on the one side, in the 
ethical systems upon which they are founded, the developmental 
force which sets in motion that life-continuing, constructive pro- 
cess which physiologists call anabolism. On the other side, and 
in conflict with it, we have in the self-assertive rationalism of the 
individual, the tendency — by itself disintegrating and destructive 
— known as catabolism. In a social system, as in any other organ- 
ism, the downward stage towards decay is probably commenced 
when the catabolic tendency begins to progressively overbalance 
the anabolic tendency. (Benjamin Kidd.) 

18. For many generations the people of the Isle of St. Kilda 
believed that the arrival of a ship in the harbor inflicted on the 
islanders epidemic colds in the head, and many ingenious reasons 
were devised why the ship should cause colds. At last it occurred 
to somebody that the ship might not be the cause of the cold, but 
that both might be eJBfects of some other common cause, and it 
was then remembered that a ship could only enter the harbor 
when there was a strong northeast wind blowing. 

19. Schwabe, observing sun-spots for many years, discovered 
that they reached a maximum, roughly speaking, once in every 
ten years. In 1851, Lamont, reviewing a series of magnetic obser- 
vations carried on from 1835 to 1850, perceived with some sur- 
prise that they gave unmistakable indications of a period of \o\ 
years, during which the range of the daily variation of the mag- 
netic needle increased and diminished once. In the following 
winter, Sir Edward Sabine, ignorant as yet of Lamont's conclu- 
sions, undertook to examine a totally different set of observations 
concerning magnetic ^storms. ' Once in about ten years magnetic 
disturbances were perceived to reach a maximum of violence and 



Questions and Exercises 473 

frequency. Sabine was the first to note the coincidence between 
this unlooked-for result and Schwabe's sun-spot period. He 
showed that, so far as observation had yet gone, the two cycles of 
change agreed perfectly both in duration and phase, maximum 
corresponding to maximum, minimum to minimum. What the 
nature of the connection could be that bound together by a common 
law effects so dissimilar was, and still remains, beyond the reach of 
well-founded conjecture; but the fact was from the first unde- 
niable. (Gierke, History of Astronomy.) 

20. Prior to 1668 the spontaneous generation of life was com- 
monly accepted by naturalists, and the origin of maggots in decay- 
ing substances was regarded as an evidence of it. But in that year 
Redi, an Italian scientist, exposed meat in jars, some of vv^hich 
were left uncovered, some covered with parchment, and others with 
wire gauze. The meat in all these vessels became spoiled, and flies, 
being attracted by the smell of decaying meat, laid eggs in that 
which was exposed, and there came from it a large crop of mag- 
gots. The meat which was covered by parchment also decayed in 
a similar manner, without the appearance of maggots within it ; and 
in those vessels covered by wire netting the flies laid their eggs upon 
the wire netting. There they hatched, and the maggots, instead 
of appearing in the meat, appeared on the surface of the wire gauze. 
From this Redi concluded that maggots arise in decaying meat 
from the hatching of the eggs of insects. (Locy, Makers of Biology.) 

21. In 1675 Leeuwenhoek discovered infusoria, or animalcula 
under the microscope, and it was thought that such minute organ- 
isms as these might be spontaneously generated, even if the larger 
were not. About 1745 Needham performed a number of experi- 
ments to test this conclusion. He extracted the juices of meat by 
boiling, enclosed them in bottles, which were carefully corked and 
sealed with mastic, then subjected the closed bottles to heat and 
set them away to cool. In due course of time, the fluids thus treated 
became infected with microscopic life, and inasmuch as he believed 



474 Questions and Exercises 

that he had killed all living germs by repeated heating, he concluded 
that the living forms had been produced by spontaneous generation. 
Spellanzani, however, thought that Needham's experiments had 
not been conducted with sufficient care. He therefore made a 
great number of similar experiments, using different kinds of infu- 
sions. But he placed them in thin flasks with slender necks, which 
were then hermetically sealed in flame, after which he immersed the 
flasks in boiling water for three quarters of an hour, in order to de- 
stroy all germs that might be contained in them. Under these con- 
ditions no infusoria appeared in them. Needham was not satisfied 
with these results, however, and objected that such a prolonged boil- 
ing would destroy not only germs, but the germinative force of the 
infusion itself. Spellanzani easily disposed of this objection by 
showing that when the infusions were again exposed to the air, no 
matter how severe or prolonged the boiling to which they had been 
subjected, the infusoria reappeared. {Ihid.) 

22. These and similar experiments proved that there is some- 
thing in the atmosphere which, unless it be removed or rendered 
inactive, produces life within nutrient fluids, but whether this 
something is solid, fluid, or gaseous did not appear from the experi- 
ments. In 1843, however, Heimholtz showed that this something 
win not pass through a moist animal membrane, as fluids and gases 
will. {Ihid,) 

23. In the '70's, the discussion of spontaneous generation having 
been revived, Tyndall showed that in an hermetically closed box, 
within which the air was what he called 'optically pure, ' or entirely 
free from all floating particles, putrescible liquids in test-tubes, 
previously sterilized, might be exposed indefinitely without spoiling. 
But on admitting the outside air even for an instant, the liquids 
within a few days were spoiled and full of micro-organisms. 
{Ihid,) 

24. Pouchet devised an experiment to prove the spontaneous 
generation of micro-organisms, in which an hermetically sealed 



Questions and Exercises 475 

vessel, previously filled with boiling water, was opened beneath the 
surface of a basin of mercury, so as to exclude all air, and some 
sterilized hay and absolutely pure oxygen, made at a temperature 
of incandescence, introduced. The infusion moulded. 

Pasteur replied to this by showing that the surface of the mercury 
was covered with minute particles of atmospheric dust. (Vallery- 
Radot, Louis Pasteur.) 

25. Pasteur took a series of bulbs of about a quarter of a litre in 
capacity, and after having half -filled them with a putrescible liquid, 
he drew out the necks by means of the blowpipe, then caused the 
liquid to boil for some minutes, and during the ebullition, while the 
steam issued from the tapering ends of the bulbs, he sealed them 
with the lamp. Thus prepared, the bulbs were easily transported. 
As they were empty of air, that which they originally contained 
having been driven off, when the sealed end was broken off, the air 
rushed into the tube, carrying with it all the germs it held in suspen- 
sion. Closing the tube immediately afterwards with a flame, and 
leaving the vessels to themselves, it was easy to recognize those 
in which a change occurred. 

Pasteur opened and resealed 20 of these bulbs in the country, far 
from all habitations; 20 more in the Jura, at 850 metres above sea- 
level; and 20 more in the Montanvert, at 2000 metres. In the 
first 20, there were 8 bulbs in which organisms appeared ; in the 
second 20, there were 5; and in the third 20, only i. (Ibid.) 

26. 'Whether or not a bad theory is better than none depends 
upon circumstances.' Examine this statement, and point out 
what are some of the circumstances of which mention is made. 

27. It is said that a general resemblance of the hills near Ballarat 
in Australia to the Californian hills where gold had been found 
suggested the idea of digging for gold at Ballarat. (Minto.) 

28. There are no great nations of antiquity but have fallen to 
the hand of time; and England must join them to complete the 
analogy of the ages. Like them she has grown from a birth-time 



4/6 Questions and Exercises 

of weakness and tutelage to a day of manhood and supremacy; 
but she has to face her setting. Everything that grows must also 
decay. (Edinburgh, 1893.) 

29. Goldscheider proved that muscular sensations play no con- 
siderable part in our consciousness of the movements of our limbs, 
by having his arm suspended in a frame and moved by an attend- 
ant. Under these circumstances, where no work devolved on 
his muscles, he found that he could distinguish as small an angular 
movement of the arm as when he moved and supported it himself. 

30. Goldscheider also proved that the chief source of move- 
ment-consciousness is pressure sensations from the inner surface 
of the joints, by having his arm held so that the joint surfaces 
were pressed more closely together, and finding that a smaller 
movement was now perceptible. 

31. Wages in the United States are higher than in England, 
because the former country is a republic and has a protective 
tariff. 

32. It does not follow that an institution is good because a 
country has prospered under it, nor bad because a country in 
which it exists is not prosperous. It does not even follow that 
institutions to be found in all prosperous countries, and not to be 
found in backward countries, are therefore beneficial. For this 
at various times might confidently have been asserted of slavery, 
of polygamy, of aristocracy, of established churches ; and it may 
still be asserted of public debts, of private property in land, of 
pauperism, and of the existence of distinctly vicious or criminal 
classes. (George.) 

33. '^No Body can be healthfull without Exercise^ neither 
Naturall Body, nor Politique : And certainly, to a Kingdome or 
Estate, a Just and Honourable Warre, is the true Exercise, A 
Civill Warre, indeed, is like the Heat of a feaver; but a Forraine 
Warre, is like the Heat of Exercise^ and serveth to keepe the Body 
in Health." (Bacon, Essays.) 



Questions and Exercises 477 

34. Explain the procedure of the reductio ad absurdum form 
of argument. 

35. It may be a coincidence merely; but, if so, it is remarkably 
strange that while the chloroform has not changed, while the con- 
stitutions of the patients have not changed, where the use of the 
inhaler is the rule, there are frequent deaths from chloroform; 
whilst in Scotland and Ireland, where the use of the inhaler is the 
exception, deaths are proportionally rare. 

36. We should think it a sin and shame if a great steamer, 
dashing across the ocean, were not brought to a stop at a signal 
of distress from the m.ere smack. . . . And yet a miner is en- 
tombed alive, a painter falls from a scaffold, a brakeman is crushed 
in coupling cars, a merchant fails, falls ill and dies, and organized 
society leaves widow and child to bitter want or degrading alms. 
(George, Protection and Free Trade.) 

37. ^^ For there are only two possible a priori explanations of 
adaptations for the naturalist; namely, the transmission of func- 
tional adaptations and natural selection; but as the first of these 
can be excluded, only the second remains." (Weismann.) 

38. The planet Mars resembles the Earth in possessing atmos- 
phere, water, and moderate temperature, and we may therefore 
suppose it to be inhabited. (St. Andrews.) 

39. Manufacturing countries are always rich countries; coun- 
tries that produce raw material are always poor. Therefore, if we 
would be rich, we must have manufactures, and in order to get 
them, we must encourage them. . . . But I could make as good 
an argument to the little town of Jamaica ... in support of a 
subsidy to a theatre, I could say to them : all cities have theatres, 
and the more theatres it has the larger the city. Look at New 
York ! . . . Philadelphia ranks next to New York in the number 
and size of its theatres, and therefore comes next to New York in 
wealth and population. ... I might then drop into statistics 
. . . and point to the fact that when theatrical representations 



4/8 Questions and Exercises 

began in this country, its population did not amount to a million, 
that it was totally destitute of railroads, and without a single mile 
of telegraph wire. Such has been our progress since theatres 
were introduced that the census of 1880 showed we had 50,155,783 
people, 90,907 miles of railroad, and 291,212^0- miles of telegraph 
wires. (George, Protection and Free Trade.) 

40. What methods would you employ to investigate the connec- 
tion between changes in the barometer and in the weather? 

41. In Sir Humphry Davy's experiments upon the decompo- 
sition of water by galvanism, it was found that, besides the two 
components of water, oxygen and hydrogen, an acid and an alkali 
were developed at the two opposite poles of the machine. The 
insight of Davy conjectured that there might be some hidden 
cause of this portion of the effect: the glass containing the water 
might suffer partial decomposition, or some foreign matter might 
be mingled with the water, and the acid and alkali be disengaged 
from it, so that the water would have no share in their production. 
... By the substitution of gold vessels for glass, without any 
change in the effect, he at once determined that the glass was not 
the cause. Employing distilled water, he found a marked diminu- 
tion of the quantity of acid and alkali evolved; yet there was 
enough to show that the cause, whatever it was, was still in opera- 
tion. . . . He now conceived that the perspiration from the 
hands touching the instruments might affect the case, as it would 
contain common salt, and an acid and an alkali would result from 
its decomposition under the agency of electricity. By carefully 
avoiding such contact, he reduced the quantity of the products 
still further until no more than slight traces of them were percep- 
tible. An experiment determined this: the machine was put 
under an exhausted receiver, and when thus secured from atmos- 
pheric influence, it no longer evolved the acid and the alkali. 
(Gore, The Art of Scientific Discovery.) 

42. In the vast majority of cases the best brain work of which in- 



Qicestions and Exercises 479 

dividuals of average or of unusual ability are capable is performed 
under conditions of imperfect health. . . . The mind at its best is 
to be found in a body that is not at its best. ... I do not think 
it can be doubted that as classes, country clergymen, army men, and 
country gentlemen enjoy a ruder health and have a less frequent 
resort to doctors and drugs than barristers, journalists, and medical 
men. The natural conditions of their lives . . . and their open- 
air habits . . . conduce to perfect health. I do not think it can be 
doubted, that as classes, clergymen, army men, and country gentle- 
men are characterized by brains less active in their higher intellectual 
functions than the brains of the less healthy professional classes. . . . 
The case for my proposition becomes even stronger when preem- 
inent brain work is considered. I cannot, at the present moment, 
recall a single great poet, man of letters or man of science, in fact, 
any person greatly distinguished by the product of his brain, who 
was a type of good health. Examples to the contrary surge into the 
mind. . . . Consider Newton, always an invalid ; Clerk Maxwell, 
who died young after a life of ill-health; Darwin, who after he 
reached adult life was probably never well for three consecutive 
days. Consider Poe and Pope, Chatterton, Keats, Shelley, Byron, 
Heine, and a thousand other poets. Consider Gibbon and Carlyle, 
De Quincey — it is needless to prolong the catalogue ; but I would 
ask readers to think over the distinguished people they know. It 
is difficult to mention the names of living distinguished persons, 
but for my own part I am certain that I do not know a single per- 
son whose intellect I respect greatly, who enjoys robust health. 
{Saturday Review.) 

43. It was formerly supposed that all the nervous fibres in the 
body exercised both the function of conveying motor stimuli to the 
muscles, and sensory stimuli to the brain. This was apparently 
confirmed by the fact that when any nerve was severed both sensation 
and motion disappeared in the part to which it led. But in 181 1, 
Sir Charles Bell published an essay to show that nerves were com- 



480 Questions and Exeixises 

posed of various filaments, whose function differed according to the 
location of their original roots in the brain or in the spinal cord. 
This theory, he pointed out, would account for the extreme com- 
plexity of the structure of the brain and of the nervous system, 
which on the older supposition remained entirely unexplained. It 
was absurd, he also maintained, to suppose that one and the same 
nerve-fibre could conduct sensory stimuli to the brain and motor 
stimuli from it at the same instant ; yet we are constantly moving 
a part at the same time that we receive sensations from it. 

44. In order to experimentally test his theory, he selected two 
of the cerebral nerves, the portio dura and the fifth pair, the first of 
which has one root, while the latter has two. On cutting the portio 
dura in a living animal, motion only was lost in the parts with which 
it communicates. The fifth pair has some branches which arise 
from only one of its roots, and some which arise from both roots. 
On cutting the first set of branches, sensation only disappeared; 
on cutting the second, both sensation and the power of motion were 
destroyed. 

45. The spinal nerves have two roots, an anterior and a posterior. 
When Bell exposed and irritated the anterior root, convulsive move- 
ments of the muscles were set up ; but on irritating the posterior 
root, no movement followed. He felt assured, therefore, that the 
motor function was confined to the fibres of the anterior root; 
but inasmuch as the operation of exposing the roots was intensely 
painful to the animal, he could not be certain that sensation was set 
up by the fibres of the posterior root only. 

46. It was pointed out, however, that in some cases of partial 
paralysis of the limbs with which these nerves communicate, motion 
alone is lost, while the power of sensation is retained ; in other cases, 
the reverse condition obtains. This seems to show — (What? and 
How?) 

47. Glaciers are ice-streams, or rivers in which the moving mate- 
rial is frozen instead of liquid water. Like large rivers, they ordi- 



Questions and Exercises 481 

narily have their sources in high mountains, and descend along the 
valleys ; but the mountains are such as to take snow from the clouds 
instead of rain, because of their elevation. Like large rivers, many 
tributary streams coming from the different valleys unite to make 
the great stream. As with rivers, their movement is dependent on 
gravity, or the weight of the material ; but the average rate of motion, 
instead of being several miles an hour, is generally in summer but 
10 to 18 inches a day, or a mile in 18 to 20 years. As with rivers, 
the central portions move most rapidly, the sides and bottom being 
retarded by friction. (J. D. Dana.) 

48. The human race, Mr. Fries contends, suffers no ill-effects 
from its meat-eating habits. Yet it is generally acknowledged that 
the human race dies very prematurely, — so prematurely, in fact, 
that a full third of people's lives is cut off entirely. It is generally 
recognized by biologists that any animal should live five times the 
length of its period of maturity; a dog matures at 2 and dies at 10, 
etc. This is the average that maybe observed throughout the animal 
kingdom. Man, it is asserted, matures at about 25, so that, by anal- 
ogy, he should live to be 125 years old — and that before he shows 
signs of decrepitude, mental or physical. Yet, in place of this, 
what do we find ? That the average term of life is something over 42 
years, and, not only that, but those 42 years are filled with sick- 
nesses and diseases of all kinds, as human experience testifies. Is 
this a normal condition ? Or is there not something wrong some- 
where to produce these results; and what so wrong and per° 
verted as the present food habits of the people? (Letter to 
N , F. Times.) 

49. {a) Moisture bedews a cold metal or stone when we breathe 
on it. The same appears on a glass of ice-water, and on the in- 
side of windows when sudden rain or hail chills the external air. 
The inference is that when an object contracts dew it is colder 
than the surrounding air. 

(&) No dew is deposited on a piece of polished metal, but on 
21 



482 Questions and Exercises 

the same metal unpolished dew is deposited copiously. There- 
fore the deposit of dew is affected by the kinds of surface exposed. 

{c) With various kinds of polished metals, no dew is deposited ; 
but with various kinds of highly polished glass dew is deposited. 
Therefore the deposit of dew is affected by the kinds of substances 
exposed. 

{d) It is known by direct experiment that for any given degree 
of temperature, only a limited amount of water can remain sus- 
pended as vapour, and this quantity grows less and less as the tem- 
perature diminishes. Therefore if there is already as much vapour 
suspended as the air will contain at its existing temperature, any 
lowering of the temperature will cause necessarily a portion of the 
vapour to be condensed as dew. (Hibben.) 

50. Properties known to exist in potassium have been predicted 
of and found to exist in rubidium ; for instance, the carbonates of 
sodium and potassium are not decomposed by a red heat, neither 
are those of rubidium, or caesium. Some of the statements which 
are true of chlorine have been found to be true, in varying degrees, 
of bromine and iodine. . . . After I had found the molecular 
change in antimony electro-deposited from its chloride, I sought 
for and discovered it in that deposited from its bromide and iodide; 
and after having found magnetic changes in iron by heat, I also 
found similar ones in nickel. (Gore, The Art of Scientific Dis- 
covery.) 

51. What inductive fallacy may David be said to have com- 
mitted when he said in his haste that all men are liars ? 

52. It has been found that linnets when shut up and educated 
with singing larks — the skylark, woodlark, or titlark — will 
adhere entirely to the songs of these larks, instead of the natural 
song of the linnets. We may infer, therefore, that birds learn to 
sing by imitation, and that their songs are no more innate than 
language is in man. (Hyslop.) 

53. We observe very frequently that very poor handwriting 



Questions and Exercises 483 

characterizes the manuscripts of able men, while the best hand- 
writing is as frequent with those who do little mental work when 
compared with those whose penmanship is poor. We may, 
therefore, infer that poor penmanship is caused by the influence 
of severe mental labour. (Hyslop.) 

54. Galileo describes his invention of the telescope as follows : 
This then was my reasoning; this instrument [of which he had 
heard a rumour] must either consist of one glass, or of more than 
one; it cannot be of one alone, because its figure must be either 
concave or convex, or comprised within two parallel superficies, 
but neither of these shapes alter in the least the objects seen, 
although increasing or diminishing them; for it is true that the 
concave glass diminishes, and that the convex glass increases 
them ; but both show them very indistinctly, and hence one glass 
is not suflicient to produce the effect. Passing on to two glasses, 
and knowing that the glass of parallel superficies has no effect at 
all, I concluded that the desired result could not possibly follow 
by adding this one to the other two. I therefore restricted my 
experiments to combinations of the other two glasses; and I saw 
how this brought me to the result I desired. (Quoted by Gore, 
The Art of Scientific Discovery^ 

55. Darwin was struck by the number of insects caught by the 
leaves of the common sun-dew. It soon became evident to him 
that '^Drosera was excellently adapted for the special purpose of 
catching insects." ... As soon as he began to work on Drosera, 
and was led to believe that the leaves absorbed nutritious matter 
from the insects, he began to reason by analogy from the well-un- 
derstood digestive capacity of animals. . . . Having by analogy 
established the power of digestion in plants, analogy led him to 
seek in plants the elements that do the work of digestion in animals. 
Bringing together what was known of plants, he pointed out that 
the juices of many plants contain an acid, and so one element of a 
digestive fluid was at hand; and that all plants possess the power 



484 Questions and Exercises 

of dissolving albuminous or proteid substances, protoplasm, chlo- 
rophyl, etc., and that ^'this must be effected by a solvent, proba- 
bly consisting of a ferment together with an acid." After writing 
the last-quoted sentence, he learned that a ferment which con- 
verted albuminous substances into true peptones had been ex- 
tracted from the seeds of the vetch. (Cramer, The Method of 
Darwin.) 

56. Strongly impressed with the belief that some '^ harmonic " 
relation must exist among the distances of the several planets 
from the sun, and also among the times of their revolution, Kepler 
passed a large part of his early life in working out a series of guesses 
at this relation, some of which now strike us as not merely most 
improbable, but positively ridiculous. His single-minded devo- 
tion to truth, however, led him to abandon each of these hypotheses 
in turn so soon as he perceived its fallacy by submitting it to the 
test of its conformity to observed facts. . . . But he was at last 
rewarded by the discovery of that relation between the times and 
the distances of the planetary revolutions, which with the dis- 
covery of the ellipticity of the orbits, and of the passage of the 
radius vector over equal areas in equal times has given him immor- 
tality as an astronomical discoverer. But ... he was so far 
from divining the true rationale of the planetary revolutions that 
he was led to the discovery of the elliptical orbit of Mars by a 
series of happy accidents . . . whilst his discovery of the true 
relations of times and distances was the fortunate guess which closed 
a long series of ^/zfortunate ones, many of which were no less 
ingenious. 

Now it was by a grand effort of Newton's constructive imagina- 
tion, based on his wonderful mastery of geometrical reasoning, 
that, starting with the conception of two forces^ one of them tend- 
ing to produce continuous uniform motion in a straight line, the 
other tending to produce a uniformly accelerated motion towards 
a fixed point, he was able to show that if these dynamical assump- 



Questions and Exercises 485 

tions were granted, Kepler ^s laws, being consequences of them, 
must be universally true. And it was his still greater glory to 
divine the profound truth that the fall of the moon towards the 
earth — that is, the deflection of her path from a tangential line to 
an ellipse — is a phenomenon of the same order as the fall of a stone 
to the ground. (Gore, The Art of Scientific Discovery.) 

57. After Franklin had investigated the nature of electricity 
for some time, he began to consider how many of the effects of 
thunder and lightning were the same as those produced by elec- 
tricity. Lightning travels in a zigzag line, and so does an electric 
spark ; electricity sets things on fire, so does lightning ; electricity 
melts metals, so does hghtning. Animals can be killed by both, 
and both cause blindness. Pointed bodies attract the electric 
spark, and in the same way lightning strikes spires, and trees, and 
mountain tops. Is it not likely then that lightning is nothing 
more than electricity passing from one cloud to another, just as an 
electric spark passes from one substance to another ? (Buckley, 
A Short History of Natural Science,) 

58. How did Franklin proceed to verify the hypothesis stated 
in the last example ? 

59. When men had formed a notion of the moon as a solid body 
revolving about the earth, they had only further to conceive it 
spherical, and to suppose the sun to be beyond the region of the 
moon, and they would find that they had obtained an explanation 
of the varying forms which the bright part of the moon assumes in 
the course of a month. For the convex side of the crescent-moon, 
and her full edge when she is gibbous, are alvv^ays turned towards 
the sun. And this explanation, once suggested, would be confirmed 
the more it was examined. For instance, if there be near us a 
spherical stone, on which the sun is shining, and if we place ourselves 
so that this stone and the moon are seen in the same direction (the 
moon appearing just over the top of the stone), we shall find that 
the visible part of the stone, which is then illuminated by the sun, 



486 Questio7is and Exercises 

is exactly similar in form to the moon, at whatever period of her 
changes she may be. (Whewell.) 

60. Not long ago the adherents of spontaneous generation urged 
as an argument on their side that if biogenesis be true, innumerable 
facts and experiments prove that the air must be thick with germs, 
and they regarded this as the height of absurdity. But that micro- 
organisms exist everywhere has since been shown beyond the 
shadow of a doubt. 

61. In every animal possessing a circulation of the blood which 
had been observed up to 1824, the current of the blood was known to 
take one definite and invariable direction. Now, there is a class of 
animals called Ascidians which possess a heart and a circulation, 
and up to this period no one would have dreamt of questioning the 
propriety of the deduction that these creatures have a circulation 
in one direction ; nor would any one have thought it worth while to 
verify the point. But in that year M. von Hasselt, happening to 
examine a transparent animal of this class, found to his infinite 
surprise that after the heart had beat a certain number of times, it 
stopped, and then began beating the opposite way — so as to re- 
verse the course of the current, which returned by and by to its 
original direction. (Huxley.) 

62. ^^Sir Oliver Lodge ... is persuaded that messages are 
received from the dead. ... Sir Oliver . . . seems an easy 
man to convince. The message — through the usual medium — 
is presumably from Frederic W. H. Myers. ... In his lifetime 
he was an essayist and poet of unusual delicacy of taste and pre- 
cision of style. ... It is painful, therefore, to ascribe to Mr. 
Myers these lines: — 

Friend, while on earth with knowledge slight, 
I had the living power to write ; 
Death tutored now in things of might, 
I yearn to you and cannot write. 

And this from a man 'of rare intellectual gifts, original, acute, 
and thoughtful' ! " (Nation) 



Questions and Exercises 487 

63. Sir Oliver Lodge replied that ^' It would be painful to attrib- 
ute (this passage) to the developed intelligence of Mr. Myers or 
any other poet. But in what evidence do you assume that we have 
done so ? Ought a schoolboy exercise in a foreign language or 
a rhyme constructed between sleep and waking to be esteemed part 
of the output of a man of letters? " (Letter to Nation.) 

64. The following is the cardinal passage in Harvey's famous 
argument for the circulation of the blood: ^'Let us assume either 
arbitrarily or from experiment, the cjuantity of blood which the 
left ventricle of the heart will contain when distended, to be, say, 
two ounces, three ounces, or one ounce and a half — in the dead 
body I have found it to hold upwards of two ounces. . . . Let us 
suppose as approaching the truth that the fourth, or fifth, or sixth, 
or even that the eighth part of its charge is thrown into the artery 
at each contraction ; this would give either half an ounce, or three 
drachms, or one drachm of blood as propelled by the heart at each 
pulse into the aorta; which quantity, by reason of the valves at 
the root of the vessel, can by no means return into the ventricle. 
Now, in the course of half an hour, the heart will have made 
more than one thousand beats, in some as many as two, three, 
and even four thousand. Multiplying the number of drachms 
propelled by the number of pulses, we shall have either one thou- 
sand half ounces, or one thousand times three drachms, or a like 
proportional quantity of blood, according to the amount which 
we assume as propelled with each stroke of the heart, sent from 
this organ into the artery; a larger quantity in every case than is 
contained in the whole body! . . . (Thus), supposing even the 
smallest quantity of blood to be passed through the heart and the 
lungs with each pulsation, a vastly greater amount would still be 
thrown into the arteries . . . than could by any possibility be sup- 
plied by the food consumed. It could be furnished in no other 
way than by making a circuit and returning." {De motu cordis, 
Ch. IX.) 



488 Questions and Exercises 

65. The older theory was that the arterial pulse served the same 
purpose as respiration. One of Harvey's arguments against this 
is as follows: ^^Now if the arteries are filled in the diastole with 
air then taken into them (a larger quantity of air penetrating when 
the pulse is strong and full), it must come to pass, that if you plunge 
into a bath of water or oil when the pulse is strong and full, it ought 
forthwith to become either smaller or much slower, since the cir- 
cumambient bath will render it either difficult or impossible for 
the air to penetrate." 

66. Galileo discovered by means of his telescope that Jupiter 
has four moons, instead of one like the earth, and he regarded 
this discovery as a confirmation of the Copernican theory. Ex- 
plain the nature of the reasoning involved in reaching this con- 
clusion. 

67. That the period of tide should be accidentally the same as 
that of the culmination of the moon, that the period of the highest 
tide should be accidentally the same as the syzygies, is possible 
in ahstracto; but it is in the highest degree improbable: the far 
more probable assumption is, either that the sun and moon pro- 
duce the tide, or that their motion is due to the same grounds as 
the motion of the tide. (Hibben.) 

68. During the retreat of the Ten Thousand a cutting north 
wind blew in the faces of the soldiers; sacrifices were offered to 
Boreas, and the severity of the wind immediately ceased, which 
seemed a proof of the god's causation. {Anabasis, Bk. IV.) 

69. A nectary implies nectar, but Sprengel had come to the 
conclusion that orchis morio and orchis maculata, though furnished 
with nectaries, did not secrete nectar. Darwin examined the 
flowers of orchis morio for twenty-three consecutive days, looking 
at them after hot sunshine, after rain, and at all hours; he kept 
the spikes in water and examined them at midnight and early the 
next morning. He irritated the nectaries with bristles, and ex- 
posed them to irritating vapours. He examined flowers whose 



Questions and Exercises 489 

pollinia had been removed, and others which would probably 
have them soon removed. But the nectary was invariably dry. 
He was thoroughly convinced, however, that these orchids 
require the visits of insects for fertilization, and that insects visit 
flowers for the attractions offered in the way of nectar, and yet 
that in these orchids the ordinary attraction was absent. In 
examining the orchids he was surprised at the degree to which 
the inner and outer membranes forming the tube or spur were 
separated from each other, also at the delicate nature of the inner 
membrane, and the quantity of fluid contained between the two 
membranes. He then examined other forms that do secrete 
nectar in the ordinary way, and found the membranes closely 
united, instead of separated by a space. ^'I was therefore led to 
conclude," he says, ^'that insects penetrate the lax membrane of 
the nectaries of the above-named orchids and suck the copious 
fluid between the two membranes." He afterwards learned that 
at the Cape of Good Hope moths and butterflies penetrate peaches 
and plums, and in Queensland a moth penetrates the rind of the 
orange. These facts merely proved his anticipation less anoma- 
lous than it had seemed. (Cramer, The Method of Darwin}} 

70. Construct an hypothesis to explain some fact of your expe- 
rience, and explain how it may be either verified or overthrown. 

71. When Darwin began to work on Drosera he was led to 
believe that the leaves absorbed nutritious matter from insects. 
He then reasoned by analogy from the well-understood digestive 
capacity of animals. He made preliminary 'crucial ' experiments 
by immersing some leaves of Drosera in nitrogenous and others 
in non-nitrogenous fluids of the same density to determine 
whether the former affected the leaves differently from the latter. 
This he found to be the case. He then experimented with solid 
animal matter and found that the leaves are capable of true diges- 
tion. Analogy then led him to seek in plants the elements that do 
the work of digestion in animals. He pointed out that the juices 



490 Questions and Exercises 

of many plants contain an acid, and so one element of a digestive 
fluid was at hand ; and that all plants possess the power of dis- 
solving albuminous or proteid substances, protoplasm, chlorophyl, 
and that this must be effected by a solvent consisting probably 
of a ferment together with an acid. Afterwards he learned that 
a ferment which converted albuminous substances into true pep- 
tones had been extracted from the seeds of the vetch. (Cramer, 
The Method of Darwin^ pp. 95-99.) 

72. In opposition to the facts stated above, Tischutkin main- 
tains that the ^digestion' of insectivorous plants is not accom- 
plished in the same way as in animals, but is due to bacteria : that 
the pepsin is not a secretion of the plant, but a by-product of the 
activity of the bacteria. Suppose that this theory is true, and 
Darwin's false, what would you say regarding the character of the 
latter's reasoning ? 

73. Vesalius, the founder of modern anatomy, found that the 
human thigh bone was straight, and not curved, as Galen, the 
great authority on the subject for over a thousand years, had 
asserted. Sylvius replied that Galen must be right ; that the bone 
was curved in its natural condition, but that the narrow trousers 
worn at the time had made it artificially straight. 

74. " From looking at species as only strongly-marked and 
well-defined varieties, I was led to anticipate that the species of 
the larger genera in each country would oftener present varieties 
than the species of the smaller genera; for wherever many 
closely related species {i.e, species of the same genus) have been 
formed many varieties or incipient species ought, as a general rule 
to be now forming. ... To test the truth of this anticipation I 
have arranged the plants of twelve countries, and the coleopterous 
insects of two districts into two nearly equal masses, the species of 
the larger genera on one side and those of the smaller genera on the 
other side, and it has invariably proved to be the case that a larger 
proportion of the species on the side of the larger genera presented 



Questions and Exercises 491 

varieties than on the side of the smaller genera. Moreover, the 
species of the large genera which present any varieties invariably 
present a larger average number of varieties than do the species of 
the small genera. Both of these results follow when another di- 
vision is made, and when all the least genera with only one to four 
species are altogether excluded from the tables. '' (Darwin, Origin 
of Species.) 

75. Sir Joseph Lister, the founder of aseptic surgery, states the 
origin of his method as follows: '^When it had been shown by the 
researches of Pasteur that the septic property of the atmosphere de- 
pended, not on oxygen or any gaseous constituent, but on minute 
organisms suspended in it, which owed their energy to their vitality, 
it occurred to me that decomposition in the injured part might be 
avoided without excluding the air, by applying as a dressing some 
material capable of destroying the life of the floating particles.'' 
At first he used carbolic acid for this purpose. The wards of Vv^hich 
he had charge in the Glasgow Infirmary were especially affected by 
gangrene, but in a short time became the healthiest in the world ; 
while other wards separated only by a passageway retained their 
infection. (Locy.) 

76. The spectroscope. . . has suggested the presence of sub- 
stances not known upon the earth. To one of these substances, indi- 
cated by a green line in the spectrum of the sun's corona, the name 
Coronium has been given provisionally. It has been suggested that 
this line may represent not a new substance, but known substances 
under the unknown conditions of the sun's temperature. However, 
as it exists at least 300,000 miles from the sun, it is impossible that 
the conditions of temperature are so entirely different from those 
known to us as completely to disguise known substances, and most 
scientists now accept the conclusion that the green line is caused by 
the presence of an element hitherto unknown in any other region of 
nature. Recently, Professor Nasini of Padua, with two colleagues, 
has been examining the gases of the volcanic regions of his country 



492 Questions and Exercises 

. . . for argon and helium (and in them) he has discovered the 
existence of coronium. {Saturday Review.) 

77. It was discovered by Arago in 1811, and by Biot in 1812 
and 18 18, that a plate of rock-crystal, cut perpendicular to the 
axis of the prism, possessed the power of rotating the plane of polar- 
ization through an angle, dependent on the thickness of the plane 
and the refrangibility of the light. It was, moreover, proved by 
Biot that there existed two species of rock-crystal, one of which 
turned the plane of polarization to the right, and the other to the left. 
No external difference of crystalline form was at first noticed which 
could furnish a clew to this difference of action. But closer scrutiny 
revealed upon the crystals minute facets, which, in the one class, 
were ranged along a right-handed, and, in the other, along a left- 
handed spiral, thus making the crystals dissymmetrical in opposite 
ways. (Tyndall, in Vallery-Radot, Louis Pasteur.) 

78. Mitscherlich brought forward the tartrates and paratartrates 
of ammonia and soda, and affirmed them to possess the same 
chemical constitution, and the same outward crystalline form, the 
tartrates, nevertheless, causing the plane of polarization to rotate 
while the paratartrates did not. It seemed to Pasteur that there 
was a profound incompatibility between the identity affirmed by 
Mitscherlich and this discrepancy of optic character. Remember- 
ing, no doubt, the observations of Biot, he instituted a search for 
facets like those discovered in rock-crystal, and which, without 
altering chemical constitution, destroyed crystalline identity. He 
found that the crystalline forms of tartaric acid and of its compounds 
presented a series of minute facets, hitherto unobserved, which made 
them right-handedly dissymmetrical. He then went on to examine 
the tartrates and paratartrates of ammonia and soda, expecting to 
find that the tartrates, like all the others, were right-handedly dis- 
symmetrical, and that the paratartrates, since they caused no 
rotation of the plane of polarization, were symmetrical. The first 
part of his expectation was verified. But he found that all the 



Questions and Exercises 493 

crystals of the paratartrate were also dissymmetrical, but that 
certain of them were so in one sense and the others in an opposite 
sense. It seemed, therefore, that the equal admixture of right- 
handed and left-handed crystals in the paratartrate, the presence of 
one exactly neutralizing the effect of the other, brought about the 
absence of rotation in the same manner as the symmetry of all 
would have done. {Ihid.) 

79. Pasteur also noticed that one of these two kinds of crystals 
of the paratartrate corresponded exactly in form with the tartrate 
prepared by means of the tartaric acid of the grape. He there- 
fore reasoned that by separating these by hand, he should be able 
to extract from them by ordinary chemical processes a tartaric 
acid identical with that of the grape, possessing all its physical, 
mineralogical and chemical properties ; and that, per contra^ from 
the second sort of crystals he should be able to extract an acid 
which should also reproduce ordinary tartaric acid, save in the one 
circumstance of possessing a dissymmetry of an inverse kind and 
exciting an action equally inverse on polarized light. Making 
the double experiment, his anticipations were realized with math- 
ematical exactitude. Before this, the existence of two types of 
tartaric acid was unknown. {Ihid.) 

80. Under the same conditions of weight, temperature, and quan- 
tity of solvent, Pasteur placed successively, in presence of the two 
acids, all the substances capable of combining with them. He found 
that all the resultant products, pair by pair, manifested exactly 
the same properties, both chemical and physical, with the single 
difference already exhibited by the two acids — that in the one case 
the deviation of the plane of polarization was to the right, while in 
the other it was to the left. (Ibid.) 

81. The idea of molecular dissymmetry, introduced by Biot, was 
forced upon Biot's mind by the discovery of a number of liquids, 
and of some vapors, which possessed the rotatory power. Some, 
moreover, turned the plane of polarization to the right, others to 



494 Questions and Exercises 

the left. Crystalline structure being here out of the question, the 
notion of dissymmetry, derived from the crystal, was transferred to 
the molecule. (Ibid.) 

82. M. Pasteur considers that his researches point to an irref- 
ragable physical barrier between organic and inorganic nature. 
Never, he says, have you been able to produce in the laboratory, by 
the ordinary processes of chemistry, a dissymmetric molecule; in 
other words, a substance which, in a state of solution, where molec- 
ular forces are paramount, has the power of causing a polarized 
beam to rotate. This power belongs exclusively to derivatives 
from the living world. (But in a number of cases) Faraday caused 
the plane of polarization in perfectly neutral (ix. non-rotating) 
liquids and solids to rotate. (And again), quartz as a crystal exerts 
a very powerful twist on the plane of polarization. Quartz dis- 
solved exerts no power at all. The molecules of quartz, then, do 
not belong to the same category as the crystal of which they are the 
constituents ; the former are symmetrical, the latter is dissymmetrical. 
This, in my opinion, is a very significant fact. By the act of crystal- 
lization, and without the intervention of life, the forces of molecules 
which are symmetrical are so compounded as to build up crystals 
which are dissymmetrical. The reasoning which applies to the 
dissymmetric crystal applies to the dissymmetric molecule. The 
dissymmetry of the latter, however pronounced and complicated, 
arises from the composition of atomic forces which, when re- 
duced to their most elementary action, are excited along straight 
lines. (Tyndall.) 

8;^. A striking characteristic of many animals, especially of cer- 
tain insects, is that they resemble or mimic other animals, or even 
inanimate objects, in a way that protects them from the attacks of 
enemies, sometimes by making them inconspicuous, sometimes by 
making them appear dangerous or unpalatable. Four causes of 
such resemblances have been proposed: (i) external or environ- 
mental causes, — food, climate, etc. ; (2) internal physiological 



Questions and Exercises 495 

causes, compelling different species to pass through similar phases ; 
(3) sexual selection; (4) natural selection. Professor Poulton, 
examining the question, reasons as follows : — 

{a) These resemblances are often to inanimate objects, — twigs, 
leaves, earth, etc. If we admitted the action of either internal or 
external causes, they might, since they would by hypothesis act alike 
on the different animals, make them resemble one another; but 
it is difficult to see why they should make them resemble lifeless 
things. As for sexual selection, that is exercised only at the mature 
stage; and these resemblances to inanimate things are very 
common in the immature stages of insects. Natural selection, 
however, explains all kinds of resemblance equally well; for 
resemblance to any object, animate or inanimate, which serves in 
any way to conceal or to protect the animal, will be a useful vari- 
ation in the struggle for life. 

(&) These resemblances, when between animals, are as often 
as not quite independent of any affinity between the species ; e.g. 
the larva of a moth looks like a wasp. But both external and 
internal causes would obviously produce the closest likeness where 
there was most physiological similarity, i.e. where the species were 
most nearly related. 

{c) The resemblances in question are not accompanied by any 
internal changes in the direction of the mimicked species except 
such as assist in producing a superficial likeness, which is the useful 
element in the result. Natural selection, by its very nature, brings 
about the retention and accumulation of useful changes only. 
Physical and internal causes would bring to pass changes of all 
sorts, superficial and deeply seated, indiscriminately. 

{d) The same resemblance is often produced in very different 
ways, in different examples of it ; for example, other insects mimic 
ants and wasps, sometimes by an actual likeness in form and move- 
ment, sometimes only by an outline strongly marked in contrasting 
colour on bodies of very different shape. But either a similar en- 



496 Questions and Exercises 

vironment or like internal causes would bring these resemblances 
about, if at all, in a uniform way. It makes no difference to 
natural selection, however, what the original causes of a resem- 
blance are ; if it is useful, any change towards it will be preserved. 
The differences in the way in which it is produced will be due to 
the orginal differences in the animals. 

{e) The food and conditions of life of many of the resembling 
species are very different. 

(/) These resemblances are far commoner in females than in 
males. Yet there is no assignable difference which would make 
them more responsive than the males to the action either of en- 
vironmental conditions or of internal causes. In fact, the female 
usually varies less from the ancestral type than the male. Such 
resemblances are more useful to the females than to the males, 
however, because of their slower flight when laden with eggs, and 
* their greater exposure to attack during egg-laying, incubation, and 
at other times. 

(^) The supposed direct effect of environment im.plies the inher- 
itance of acquired characters, which has never been satisfactorily 
proved to take place. (Poulton, Essays on Evolution, VIII, IX.) 

84. Announcement was made by Professor T. J. J. See, astron- 
omer in charge of the Naval Observatory at Mare Island, that he 
has mathematically proved that the moon is a planet captured by the 
earth from space, and not a detached portion of our globe. He re- 
jects entirely the long-accepted theories of Laplace and Sir George 
Darwin ascribing earthly origin to the moon, and asserts that his 
discovery is supported by rigorous mathematical proof. Professor 
See's announcement was made in a paper presented to the meeting 
of the Astronomical Society of the Pacific Coast, and is a further 
development of his theory, promulgated last January, that all planets 
and satellites are captured bodies which have since had their orbits 
reduced in size and rounded up under the secular action of the 
nebular-resisting medium once pervading the solar system. In his 



Questions and Exercises 497 

former paper presenting this theory Professor See' showed how 
the satelHtes, or the material of them which once revolved around 
the sun, as the asteroids now do, got shifted into orbits about the 
planets. He has now explained the origin of the moon in the same 
way, and in his paper he explains the famous outstanding inequality 
of six seconds in the secular acceleration of the moon's mean 
motion. He says this perturbation in the moon's motion had 
been discovered by Halley in the time of Newton. It was 
partially explained by Laplace in 1787, but gravity alone 
would not account for the observed acceleration since the time 
of the Chaldeans, 720 B.C., and the outstanding difference had 
perplexed the greatest mathematicians for more than a century. 
Having discovered that the moon was originally captured and was 
still slowly nearing the earth. Professor See says he has removed the 
last difficulty, and the result would be decided improvement in 
astronomy. {N , Y. Times.) 

85. In 1838 Schleiden, who had been studying the cellular 
structure of plants under the microscope, communicated his observa- 
tions to Schwann. He mentioned in particular the nucleus and 
its relationship to the other parts of the cell. Schwann was at 
once struck by the fact that he had found similar nuclei in the 
elements of animal tissue. Schleiden also recognized these nuclei 
as in effect the same on being shown Schwann's sections, and the 
latter was thus aided to come to the conclusion that the elements in 
animal tissue were practically identical with those of plant tissue. 

86. In 1835, before this cell theory was announced, living matter 
had been observed by Dujardin. In lower animal forms he noticed 
a semifluid, jelly-like substance, which he designated sarcode, 
and which he described as being endowed with all the properties of 
life. He observed it very carefully in different forms of the in- 
vertebrates, not only as to its structure, but also as to its chemical 
properties, which distinguished it from albumen, mucus, gelatin, and 
other like substances. Dujardin was far from appreciating the full 

2K 



49^ Questions and Exercises 

importance of his discovery, and for a long time his description of 
sarcode remained separate; but in 1846 Hugo von Mohl, a 
botanist, observed a similar jelly-like substance in plants, which he 
called plant-slime, and to which he attached the name of protoplasm. 
On the basis of these observations, and of his own study of the 
movements of the spores of one of the simplest plants, Cohn, in 
1850, declared that vegetable protoplasm and animal sarcode, 
if not identical, were at least in the highest degree analogous 
substances. Finally, in 1861, Max Schultze showed that sarcode, 
which was supposed to be confined to the lower invertebrates, was 
present also in the tissues of higher animals, and there exhibits the 
same properties, especially those of contractility and irritability. 
He showed also that sarcode agreed in physiological properties 
v/ith protoplasm in plants, and that the two living substances were 
practically identical. It v/as on physiological likeness, rather than 
on structural or chemical grounds, that he based his sweeping con- 
clusions. He therefore defined both plant and animal cells as 
little masses of protoplasm surrounding a nucleus. 

87. On the basis of continued microscopic study during the 
years intervening, Verworn, in 1895, redefined a cell as ^^a body 
consisting essentially of protoplasm in its general form, including 
the unmodified cytoplasm, and the specialized nucleus and cen- 
trosolne ; while as unessential accompaniments may be enumerated 
(i) the cell membrane, (2) starch grains, (3) pigment granules, 
and (4) chlorophyl granules." 

%Z. Meanwhile, the cell has come to be regarded not only as the 
element of structure, but also as the unit of physiological activities, 
and the conveyer of hereditary qualities. It is seen that all life, 
both in plants and in animals, arises from cells ; and that where 
sexual reproduction takes place, in the plant and the animal alike, 
both the ^gg and its fertilizing agents are modified cells of the 
parents' bodies. Therefore the cell is the only possible agent of 
heredity. And by microscopic observation of fertilized ova, it has 



Questions and Exercises 499 

been determined that half of their chromosomes are derived from 
the male cell and half from the female, — each egg thus containing 
hereditary substance derived from, both parents. (Locy, Chs. 
XI, XII.) 

89. In 1620 Jean Tarde argued that because the sun is ^'The eye 
of the world," and the eye of the world cannot suffer from ophthal- 
mia, sun-spots must be due not to actual specks or stains on the 
bright solar disk, but to the transits of a number of small planets 
across it. To this new group of heavenly bodies he gave the 
name of "Borbonia Sidera." 

Most of those who were capable of thinking at all on such sub- 
jects adhered either to the theory that the spots were clouds, or 
that they were slag thrown up in solar conflagrations. 

In the following century, Derham gathered from observations 
carried on during the years 1 703-1 711, ^^That the spots on the sun 
are caused by the eruption of some new volcano therein." La- 
lande upheld the view that the spots were rocky elevations uncov- 
ered by the casual ebbing of a luminous ocean. This view had 
even less to recommend it than Derham's volcanic theory. Both 
were, however, significant of a growing tendency to bring solar 
phenomena within the compass of terrestrial analogies. (Gierke, 
History of Astronomy?) 

90. In November, 1769, a spot of extraordinary size engaged 
the attention of Alexander Wilson, Professor of Astronomy in the 
University of Glasgow. He watched it day by day, and as the 
great globe slowly revolved, carrying the spot towards its western 
edge, he was struck with the gradual contraction and final disap- 
pearance of the penumbra on the side near the centre of the disk, 
and when on the 6th of December the same spot reemerged on 
the eastern limb, he perceived, as he had anticipated, that the 
shady zone was now deficient on the opposite side, and resumed 
its original completeness as it returned to a central position. 
Similar perspective effects were visible in numerous other spots 



500 Questions and Exercises 

subsequently examined by him, and he was thus in 1774 able to 
prove by strict geometrical reasoning that such appearances were, 
as a matter of fact, produced by vast excavations in the sun's 
substance. In 1861 De la Rue obtained a stereoscopic view of a 
sun-spot which confirmed Wilson's inference as to their depressed 
nature. {Ibid.) 

91. The older explanation of fermentation, espoused especially 
by the great chemist Liebig, was that it was due to the breaking 
up of nitrogenous substances under the influence of the oxygen 
of the air. ^'The ferments," said Liebig, ^'are all nitrogenous 
substances, or the liquids which embrace them, in a state of altera- 
tion which they undergo in contact with the air." It was further 
noted that fermentable substances which had been preserved for 
some time unaltered, in sealed vessels, fermented at once on expo- 
sure to the air. 

Consequently, when Cagniard-Latour and Schwann discov- 
ered the yeast-plant, Liebig, carrying general opinion along with 
him, contended that it is not because of its being organized that 
yeast is active, but because of its being nitrogenous substance in 
contact with air. It is the dead portion of the yeast — that which 
has lived and is in the course of alteration — which acts upon the 
sugar, he thought. And as in other fermentations the existence of 
an organism had not been discovered, its presence in alcoholic 
fermentation might be regarded as an incident pecuhar to this. 
(Vallery-Radot, Louis Pasteur.) 

92. It had been noticed in Germany that a solution of the 
impure commercial tartrate of lime, mingled with organic matter, 
fermented on being exposed to summer heat. On this hint, 
Pasteur prepared some pure, right-handed tartrate of ammonia, 
mixed with it albuminous matter, and found that the mixture 
fermented. His solution, at first limpid, became turbid. Search- 
ing for the cause of the turbidity, he found it to be due to the multi- 
plication of a microscopic organism, which found in the liquid 



Questions and Exercises 50 1 

its proper food. Pasteur held that this organism was a living 
ferment, a conclusion which was strengthened, if not prompted, 
by the previous discovery of the yeast-plant. (Tyndall, ibid) 

93. Pasteur next performed a similar experiment with a solu- 
tion of the paratartrate of ammonia. Owing to the opposition of 
its two classes of crystals, a solution of this salt, it will be remem- 
bered, does not turn the plane of polarized light either to the left 
or to the right. Soon after fermentation had set in, a rotation to 
the left was noticed. This rotation increased by degrees, and 
reached its maximum at the time that the fermentation was en- 
tirely completed. It was then found that all the right-handed 
tartrate had disappeared from the liquid. The organism thus 
proved itself competent to select its own food. It found, as it were, 
one of the tartrates more digestible than the other, and appropri- 
ated it, to the neglect of the other. 

With true scientific instinct, Pasteur closed with the conception 
that ferments are, in all cases, living things, and that the substances 
formerly regarded as ferments are, in reality, the food of the fer- 
ments. Touched by this v/and, difficulties fell rapidly before him. 
He proved the ferment of lactic acid to be an organism of a certain 
kind. The ferment of butyric acid he proved to be an organism 
of another kind. (Tyndall, ibid?^ 

94. In order to prove his own theory, and to disprove the asser- 
tion of Liebig that the presence of nitrogenous albumenoid matter 
was essential to fermentation, Pasteur performed three series of 
experiments: (i) The arguments of Liebig derived great strength 
from the belief which was shared by all chemists that the cells of 
yeast perish during fermentation and form lactate of ammonia. 
On examination, Pasteur found that not only was there no am- 
monia formed during alcoholic fermentation, but that even if 
ammonia were added, it disappeared, entering into the formation 
of new yeast-cells. (2) He introduced into a pure solution of 
sugar a small quantity of crystallizable salts of ammonia, and some 



502 Questions and Exercises 

phosphates of potash and magnesia. In this solution, in which 
nitrogenous matter was not present, he placed a minute quantity of 
fresh cells of yeast. The cells thus sown multiplied, and the 
sugar fermented. (3) He set up lactic acid fermentation in 
another non-nitrogenous solution. {Ibid.) 

95. The phenomena of fermentation are in a sense phenomena 
of nutrition. The organism eats, if one may say so, one part of 
the fermentable matter. But there is a striking difference between 
this and the nutrition of the higher animals, in the fact that the 
ferment, while nourishing itself with fermentable matter, decom- 
poses a quantity great in proportion to its own individual weight. 
In reflecting on this difference, it seemed to Pasteur that there 
were two facts which had much bearing upon it. It is well known 
that the most vigorous fermentation, as, for example, that of beer 
or of wine, takes place in vessels from which the air is excluded; and 
Pasteur had discovered that the butyric acid ferment not only 
lives without free oxygen, but is killed by its admission. Is there 
not, he asked, a relation between the property of being a ferment 
and the faculty of living without free oxygen? 

In order to test this conclusion, he set up a fermentation of the 
must of beer and that of grapes in shallow vessels exposed to the 
air. He found that the yeast-plant grew much more than in the 
deep vats, but that the proportion of the weight of the decomposed 
sugar to that of. the yeast formed was much decreased. While, 
for example, in the deep vats a kilogram of ferment sometimes 
decomposes 70-150 kilograms of sugar, in the shallow vessel open 
to the air i kilogram of yeast corresponds to only 5-6 of decom- 
posed sugar. In other words, the more free oxygen the yeast fer- 
ment consumes, the less is its power as a ferment ; and the surplus 
of material decomposed, over and above the actual nutriment of 
the plant, must be broken down by it in order to obtain the oxygen 
which it needs. (Ibid.) 

96. Wine exposed to air becomes vinegar. Pasteur found that 



Questions and Exercises 503 

this change was caused by a small organism, the mycoderma aceti. 
That this organism was present in the process had long been 
known, but Liebig denied that it had anything essential to do in it. 
The true cause, he asserted, was the nitrogenous matter present in 
the wine. In proof of this, he pointed to the following experi- 
ment : If a solution of pure alcohol and water, of the same alcoholic 
strength as wine, be exposed to the air, even for years, it will not 
acetify. But if a small quantity of any nitrogenized substance be 
added to it, the change to vinegar then takes place. 

Pasteur, however, repeated this experiment, adding to the solu- 
tion, instead of nitrogenous substance, a small quantity of saline 
crystals capable of sustaining plant life. Acetification took place, 
and the development of the mycoderm could be seen. (Ibid.) 

97. Pasteur showed that oxygen is taken from the air during 
acetification by the following experiment. A bottle being par- 
tially filled with wine, and then hermetically sealed, the wine 
presently changes to vinegar. If the cork be then withdrawn under 
the surface of water, water rushes in to fill precisely one-fifth of 
the space originally occupied by air. But air is composed of one 
part of oxygen to four parts of nitrogen. Further the gas left in 
the bottle has all the properties of nitrogen. (Ibid.) 

98. Newton showed that the bodies known as comets obey the 
law of gravitation ; but it was by no means certain that the indi- 
vidual of the species observed by him in 1680 formed a permanent 
member of the solar system. With another comet, however, 
which appeared in 1682, the case was different. Edmund Halley 
calculated the elements of its orbit on Newton's principles, and 
found them to resemble so closely those arrived at for comets 
observed by Peter Apian in 1531, and by Kepler in 1607, as almost 
to compel the inference that all three apparitions were of a single 
body. This implied its revolution in a period of about seventy- 
six years, and Halley accordingly fixed its return for 1 758-1 759. It 
punctually reappeared on Christmas Day, 1758, and effected its 



504 Questions and Exercises 

perihelion passage on the 12th of March following, thus proving 
beyond dispute that some at least of these erratic bodies are 
domesticated within our system, and strictly conform to its funda- 
mental laws. (Gierke.) 

99. Periodical comets are evidently bodies which have lived, each 
through a chapter of accidents; and a significant hint as to the 
nature of their adventures can be gathered from the fact that their 
aphelia are pretty closely grouped about the tracks of the major 
planets. Halley's, and four other comets, are thus related to Nep- 
tune; eight connect themselves with Uranus, nine with Saturn, 
twenty-five at least with Jupiter. Some form of dependence is 
plainly indicated, and recent researches leave scarcely a doubt that 
the ^capture-theory' represents the essential truth in the matter. 
The original parabolic paths of these comets were then changed 
into ellipses by the backward pull of a planet, whose sphere of 
influence they chanced to enter when approaching the sun from 
outer space. Moreover, since a body thus affected should neces- 
sarily return at each revolution to the scene of encounter, the same 
process of retardation may, in some cases, have been repeated 
many times, until the more restricted cometary orbits were reduced 
to their present dimensions. {Ihid.) 

100. Observations of Halley's comet have entirely disproved 
the hypothesis (designed to explain the invariability of the planetary 
periods) of what may be described as a vortex of attenuated matter 
moving with the planets, and offering, consequently, no resistance 
to their motion. For since Halley's comet revolves in the opposite 
direction to the planets, it is plain that if compelled to make head 
against an ethereal current, it would rapidly be deprived of the 
tangential velocity which enables it to keep at its proper distance 
from the sun, and would thus gradually but conspicuously ap- 
proach, and eventually be precipitated upon it. No such effect, 
however, has in this crucial instance been detected. {Ihid.) 

loi. In 1837 Bassi investigated the disease of silkworms, and 



Questions and Exercises 505 

showed that the transmission of that disease was the result of the 
passing of minute glittering particles from the sick to the healthy. 
Upon the basis of Bassi's observation, the distinguished anato- 
mist Henle, in 1840, expounded the theory that all contagious 
diseases are due to microscopic germs. 

The theory, however, was not experimentally proved until 
1877. In that year Pasteur and Robert Koch showed the direct 
connection between certain microscopic filaments and the disease 
of splenic fever, which attacks sheep and other cattle, Koch was 
able to get some of the minute filaments from diseased cattle under 
the microscope, and to trace upon a warm stage the different 
steps in their germination. He saw the spores bud and produce 
filamentous forms. They were, therefore, living organisms. 
He was able to cultivate these upon a nutrient substance, gelatin, 
and in this way to obtain a pure culture of the organism, which is 
called anthrax. He inoculated mice with the pure culture of 
anthrax germs, and produced splenic fever in the inoculated. He 
was able to do this through several generations of mice. (Locy.) 
• 102. Koch insisted that there are four necessary steps in the 
proof that any organism is the cause of a particular disease. These 
are : First, that a microscopic organism of a particular type should 
be found in great abundance in the blood and the tissue of the sick 
animal; second, that a pure culture should be made of the sus- 
pected organism; third, that this pure culture, when introduced 
into the body of another animal, should produce the disease ; and 
fourth, that in the blood and tissues of that animal there should be 
found quantities of the suspected organism. {Ihid.) 

103. Koch found that, while guinea-pigs, mice, and other ani- 
mals were killed by inoculation with anthrax, birds were not 
affected. This invulnerability had very much struck Pasteur 
and his two assistants. What was it in the body of a fowl that 
enabled it thus to resist inoculations of which the most infini- 
tesimal quantity sufficed to kill an ox ? They proved by a series 



5o6 Questio7is and Exercises 

of experiments that the microbe of splenic fever does not develop 
when subjected to a temperature of 44^ Centigrade. Now, the 
temperature of birds being between 41 and 42°, may it not be, 
said Pasteur, that the fowls are protected from the disease because 
their blood is too warm? Might not the vital resistance encoun- 
tered in the living fowl suffice to bridge over the small gap between 
41-42°, and 44-45° ? . . . This idea conducted Pasteur and his 
assistants to new researches. ^If the blood of a fowl were cooled,' 
they asked, ^ could not the splenic fever parasite live in this 
blood ?' The experiment was made. A hen was taken, and 
after inoculating it with splenic fever blood, it was placed with 
its feet in water at 25°. The temperature of the blood of the hen 
went down to 37 or 38°. At the end of twenty-four hours the hen 
was dead, and all its blood was filled with splenic fever bacteria. 
But if it was possible to render a fowl assailable by splenic fever 
simply by lowering its temperature, is it not also possible to restore 
to health a fowl so inoculated by warming it up again ? A hen 
was inoculated, subjected, like the first, to the cold-water treat- 
ment, and when it became evident that the fever was at its height' 
it was taken out of the water, wrapped carefully in cotton wool, 
and placed in an oven at a temperature of 35°. Little by little 
its strength returned; it shook itself, settled itself again, and in a 
few hours was fully restored to health. The microbe had disap- 
peared. Hens killed after being thus saved, no longer showed the 
slightest trace of splenic organisms. There have been great 
discussions in Germany and France upon a mode of treatment in 
typhoid fever, which consists in cooling the body of the patient 
by frequently repeated baths. The possible good effects of this 
treatment may be understood when viewed in conjunction with the 
foregoing experiment on fowls. In typhoid fever the cold arrests 
the fermentation, which may be regarded as at once the expres- 
sion and the cause of the disease, just as, by an inverse process, 
the heat of the body arrests the development of the splenic fever 
microbe in the hen. (Vallery-Radot, Louis Pasteur.) 



Questions and Exercises 507 

104. In 1865 Pasteur undertook the investigation of the silk- 
worm disease which was ruining the silk industry of France. The 
presence of vibratory corpuscles in the blood of the diseased 
worms was already known, and he was prepared by his previous 
discoveries of the micro-organisms which cause fermentation to 
see in these corpuscles the cause of the disease. 

By the use of the microscope, he secured a number of healthy 
worms, free from corpuscles. He prepared two infusions, one by 
pounding up a diseased worm in water, the other by pounding up 
a healthy worm. These infusions were then brushed over mul- 
berry leaves, separately, and the healthy worms were allowed to 
feed, some on the first bed of leaves, the others on the second. 
The first group of worms became diseased, the second remained 
healthy. 

It was further established, by observation of the diseased worms, 
that in the first stages of the disease, when they cannot readily be 
distinguished from the healthy, these corpuscles are confined to the 
intestines. As the disease progresses and becomes obvious, they 
are found in the other tissues ; and at death the body is full of 
them. 

Separating, therefore, the uninfected moths from the infected, 
by the use of the microscope, taking care that the food should be 
free of infection, the progeny of the former were found to be 
always free from the disease, and that of the latter to be always 
diseased. (Vallery-Radot, Louis Pasteur.) 

105. The first to employ the prism in the examination of various 
flames was a young Scotchman named Thomas Melvill. He 
studied the spectrum of burning spirits, into which were intro- 
duced successively sal ammonia, potash, etc., and noticed the 
singular predominance, under almost all circumstances, of a par- 
ticular shade of yellow light, taking up a perfectly definite and 
invariable position in the spectrum. Fraunhofer, the great 
Munich optician, later rediscovered Melvill's deep yellow ray and 



5o8 Qicestions and Exercises 

measured its place in the colour scale. It has since become well 
known as the ^sodium line,' and has played a very important 
part in the history of spectrum analysis. Nevertheless, its 
ubiquity and conspicuousness long impeded progress. 

It was because of this perplexing fact that Fox Talbot hesitated 
in 1826 to announce his theory that the presence in the spectrum 
of any individual ray told unerringly of the volatilization in the 
flame under scrutiny of some body as whose badge or distinctive 
symbol that ray might be regarded. The yellow ray appeared 
indeed without fail where sodium was; but it also appeared where 
it might be thought only reasonable to conclude that sodium was 
not. Nor was it until thirty years later that William Swan, by 
pointing out the extreme delicacy of the spectral test, and the 
singularly wide dispersion of sodium, made it appear probable 
(but even then only probable) that the questionable yellow line 
was really due invariably to that substance. Common salt (chlo- 
ride of sodium) is, in fact, the most diffusive of solids. It floats 
in the air; it flows with water; every grain of dust has its attend- 
ant particle; its absolute exclusion approaches the impossible. 
And withal, the light that it gives in burning is so intense and con- 
centrated, that if a single grain be divided into 180 million parts, 
and one alone of such inconceivably minute fragments be present in 
a source of light, the spectroscope will show unmistakably its 
characteristic beam. (Gierke.) 

106. In 1859 Kirchhoff and Bunsen entered on a long series of 
stringent and precise experiments, as a result of which they were 
able to state positively that certain rays in the spectrum are neces- 
sarily and invariably connected with certain kinds of matter. 
The assurance of their conclusion was rendered doubly sure by the 
discovery, through the peculiarities of their light alone, of two 
new metals, named from the blue and red rays by which they 
were respectively distinguished, ^Caesium' and ^Rubidium.' 
Both were immediately afterwards actually obtained in small 



Questions and Exercises 509 

quantities by evaporation of the Dlirkheim mineral waters. 
{lUd) 

Fraunhofer in 181 5, by means of a slit and a telescope, made the 
surprising discovery that the solar spectrum is crossed, not by 
seven, but by thousands of obscure transverse streaks. Of these 
he counted some 600, and carefully mapped 324. The same sys- 
tem of examination applied to the rest of the heavenly bodies 
showed the mild effulgence of the moon and the planets to be defi- 
cient in precisely the same rays as sunlight; while in the stars it 
disclosed the differences in likeness which are always an earnest 
of increased knowledge. 

One solar line especially — that marked in his map with the 
letter D — proved common to several of the stars examined ; and 
it was remarkable that it exactly coincided in position with the con- 
spicuous yellow beam which he had already found to accompany 
most kinds of combustion. Moreover, both the dark solar and the 
bright terrestrial ' D-lines ' were displayed by his refined appliances 
as double. In this striking correspondence was contained the very 
essence of solar chemistry ; but its true significance did not become 
apparent until long afterwards. (Ibid.) 

107. The ^ fixed lines' (as they were called) of the solar spectrum 
took up the position of a standing problem. One view was that the 
atmosphere of the earth was the agent by which sunlight was 
deprived of its missing beams. For some of them this is actually the 
case. Brewster found in 1832 that certain dark lines, which were 
invisible when the sun stood high in the heavens, became in- 
creasingly conspicuous as he approached the horizon. These are 
the well-known ' atmospheric lines ' ; but the immense majority of 
their companions in the spectrum remain quite unaffected by the 
thickness of the stratum of air traversed by the sunlight containing 
them. (Ibid.) 

108. There remained the true interpretation — absorption in 
the sun's atmosphere; and this^ too, was extensively canvassed. 



510 Questions and Exercises 

But a remarkable observation made by Professor Forbes of Edin- 
burgh on the occasion of the annular eclipse of May 15, 1836, 
appeared to throw discredit upon it. If the problematical dark 
lines were really occasioned by the stoppage of certain rays through 
the action of a vaporous envelope surrounding the sun, they 
ought, it seemed, to be strongest in light proceeding from his edges, 
which, cutting that envelope . obliquely, passed through a much 
greater depth of it. But the circle of light left by the interposing 
moon, and of course derived entirely from the rim of the solar disk, 
yielded to Forbes's examination precisely the same spectrum as 
light coming from its more central parts. This circumstance 
helped to baffle inquirers, already sufficiently perplexed. It still 
remains an anomaly, of which no complete explanation has been 
offered. (Ibid.) 

109. Convincing evidence as to the true nature of the solar lines 
was however at length, in the autumn of 1859, brought forward at 
Heidelberg. Kirchhoff 's experiment in the matter was a very simple 
one. He threw bright sunshine across a space occupied by vapour 
of sodium, and perceived with astonishment that the dark Fraun- 
hofer line D, instead of being effaced by flame giving a luminous 
ray of the same refrangibility, was deepened and thickened by the 
superposition. He tried the same experiment, substituting for 
sunbeams light from a Drummond lamp, and with similar result. 
A dark furrow, corresponding in every respect to the solar D-line, 
was instantly seen to interrupt the otherwise unbroken radiance of 
its spectrum. The inference was irresistible, that the effect thus 
produced artificially was brought about naturally in the same way, 
and that sodium formed an ingredient in the glowing atmosphere 
of the sun. 

This first discovery was quickly followed up by the identification 
of numerous bright rays in the spectra of other metallic bodies 
with others of the hitherto mysterious Fraunhofer lines. Kirchhoff 
was thus led to the conclusion that (besides sodium) iron, magne- 



Questions and Exercises 511 

slum, calcium, and chromium are certainly solar constituents, and 
that copper, zinc, and nickel are also present, though in smaller 
quantities. 

These memorable results were founded upon a general principle 
first enunciated by Kirchhoff, which may be expressed as follows : 
Substances of every kind are opaque to the precise rays which they 
emit at the same temperature ; that is to say, they stop the kinds of 
light or heat which they are then actually in a condition to 
radiate. {Ibid.) 

no. When a tree, or a bundle of wheat or barley straw, is burnt, 
a certain amount of mineral matter remains in the ashes — ex- 
tremely small in comparison with the bulk of the tree or of the 
straw, but absolutely essential to its growth. In a soil lacking, or 
exhausted of, the necessary mineral constituents, the tree cannot 
live, the crop cannot grow. Now contagia are living things, which 
demand certain elements of life just as inexorably as trees, or 
wheat, or barley ; and it is not difficult to see that a crop of a given 
parasite may so far use up a constituent existing in small quantities 
in the body, but essential to the growth of the parasite, so as to 
render the body unfit for the production of a second crop. The 
soil is exhausted, and, until the lost constituent is restored, the body 
is protected from any further attack of the same disorder. Such 
an explanation of non-recurrent diseases naturally presents itself 
to a thorough believer in the germ theory. . . . To exhaust a soil, 
however, a parasite less vigorous and destructive than the really 
virulent one may suffice ; and if, after having by means of a feebler 
organism exhausted the soil, without fatal result, the most highly 
virulent parasite be introduced into the system, it will prove power- 
less. This, in the language of the germ theory, is the whole secret of 
vaccination. (Tyndall.) Have you any remarks to make on this 
explanation ? 

III. A great number of contagious diseases are non-recurrent; 
an individual who has had one of them once is not likely to have it 



512 Questions and Exercises 

again. What explanation can be given of this fact? or of the fact 
that vaccination, itself a disease, preserves from the smallpox? 
After dwelling long on these facts this question arose in Pasteur's 
mind : If contagious maladies do not repeat themselves, why should 
there not be found for each of them a disease different from them, 
but having some likeness, which, acting upon them as cow-pox 
does upon smallpox, would have the virtue of a prophylactic? 

In experimenting with successive cultures of the fowl cholera 
germ, he found that while those made at short intervals killed the 
birds inoculated with it within twenty-four or forty-eight hours, a 
culture which had remained for three months in a flask with a 
stopper of cotton wool, which allows nothing but pure air to pass 
through it, not only did not kill the birds inoculated with it, but 
that when such birds were reinoculated with fresh and strong virus 
they did not die. The conclusion w^as simple: the disease can 
protect from itself. It has evidently that characteristic of virulent 
diseases, that it cannot attack a second time. Pasteur had suc- 
ceeded in producing a vaccine for fowl cholera. (Vallery-Radot.) 

112. What is it that weakens the virus during the interval 
intentionally placed between two successive cultivations, so as to 
produce the vaccine ? The oxygen of the air. For if the cultiva- 
tion of this microbe is carried on in a tube containing very little 
air, and if the tube is then closed by the flame of a lamp, the mi- 
crobe, by its development and life, quickly appropriates all the 
free oxygen contained in the tube, as well as the oxygen dissolved 
in the liquid. Thus, completely protected from contact with 
oxygen, the microbe does not become sensibly weakened for 
months, sometimes for years. {Ihid.) 

113. Pasteur now turned his attention to discovering, if possible, 
a similar vaccine against splenic fever in cattle. In the course of 
his investigations he discovered that this disease was non-recurrent, 
and he was therefore confident that such a vaccine could be found. 
He cultivated the microbe, and exposed it to the oxygen of the air 



Questions and Exercises 51 3 

at a temperature which prevented the formation of spores — for 
these would protect it from the oxygen. The resulting weakened 
culture protected the animals inoculated with it from the fever. 
114. Pasteur's discovery of a splenic fever protective virus 
was doubted, and on the invitation of an Agricultural Society he 
performed a public experiment at Melun. On May 5, 1881, 
24 sheep, 6 cows, and i goat were inoculated with five drops of 
an attenuated splenic virus. On May 17 they reinoculated 
these 31 animals with an attenuated virus, which was, however, 
stronger than the preceding one. Finally, on May 31, very 
virulent inoculation was administered to these 31 animals, and 
also to 25 sheep and 4 cows which had not previously been inocu- 
lated. On June 2, out of the 25 sheep which had not been vac- 
cinated, 21 were dead; the goat was also dead; 2 other sheep were 
dying, and the last was certain to die that evening. The non-vac- 
cinated cows had all voluminous swellings at the point of inocula- 
tion, behind the shoulder. The fever was intense, and they had no 
longer strength to eat. The vaccinated sheep were in full health. 
The vaccinated cows showed no tumour; they had not even 
suffered an elevation of temperature, and they continued to eat 
quietly. {Ibid.) 

PART III. — The Nature of Thought 
Chapter XXL — Judgment the Elementary Process 

1. What objections are there to speaking of thought as 'a thing 
like other things' ? 

2. What is the general law of Evolution ? Explain what is 
meant by a change from the homogeneous to the heterogeneous. 

3. What general conclusions are reached by the application of 
the law of Evolution to the thought-process ? 

4. What do you understand by Judgment ? How does a 
simple judgment differ from sensation ? 

2 L 



5 14 Questions and Exercises 

5. In what sense may our judgments be said to be the union 
of two concepts ? 

6. Would the doctrine that in knowing we first have Simple 
Apprehension, then as separate intellectual processes, Judgment 
and finally Inference, agree with the general evolutionary view 
of consciousness? Explain fully. 

Chapter XXII. — The Characteristics of Judgment 

1. What do you understand by the universality of judgments ? 
What is the distinction between the universahty of a judgment 
and that of a proposition? 

2. How would you prove that all judgments are universal? 

3. Is any judgment necessary in itself? If not, whence do 
judgments derive their necessity? 

4. What is the argument by which -it has been maintained that 
there must be judgments or principles which are in themselves 
necessary? How would you reply to this argument? 

5. Explain how it is possible for a judgment to be at once both 
analytic and synthetic. 

6. Explain what is meant by a ^system' of knowledge. 

7. When judgment brings new facts into relation to what we 
already know, does the old body of knowledge itself undergo 
any modification? 

Chapter XXIII. — The Laws of Thought 

1. In what sense can we speak of a law of Thought? 

2. Explain what is meant by the law of Identity. 

3. How has this law been interpreted by Boole and Jevons ? 

4. What does Jevons mean by the 'substitution of similars,' 
and how does he propose to employ this principle? 

5. What objections are there to employing the sign of equality 
to represent the relation between the subject and predicate of a 
judgment ? ' 



Questions and Exercises 515 

6. Explain how the law of Identity is related to the character- 
istics of judgment treated in the last chapter. 

7. What is the meaning of the law of Contradiction? 

8. Explain the use of the law of Excluded Middle. 

9. In what general postulate of thought is the meaning of all 
these laws included ? 

Chapter XXIV. — Types of Judgment 

1. Why do we begin with judgments of Quality ? 

2. Explain how we pass in the development of intelligence 
from Quality to Quantity. 

3. In what sense is it true that judgments of Quantity never 
give us the real nature of things, but only their relation to some- 
thing else? 

4. What is meant by anthropomorphic causes? How are 
they distinguished from scientific causes? What is meant by 
Animism ? 

5. What new element did the discovery of the law of the Con- 
servation of Energy introduce in the causal conception as em- 
ployed in certain sciences ? 

6. Why cannot this new extension have any application in the 
field of the mental sciences ? 

7. How does the standpoint of judgments of Individuality 
differ from that of judgments of Causality ? What is meant by 
an ^ infinite regress ' ? 

Chapter XXV. — Inference 

1. How does Inference differ from Judgment? In what sense 
may it be said that it is an extension of the latter process ? 

2. Does the passage from Judgment to Inference illustrate the 
general law of Logical Evolution? Explain. 

3. In the development of our knowledge, which usually comes 
""Tst, premises or conclusion? 



5i6 Questions and Exercises 

4. How is it possible to pass from the known to the unknown? 

5. Explain under what circumstances only an Inference is 
possible. 

6. What is the common element in both Induction and Deduc- 
tion? How do they differ? 

Chapter XXVI. — ■ The Unification of Knowledge 

1. Explain the distinction between ' Science ' and ^the sciences.' 

2. What part does philosophy play in the progress of knowledge 
toward unity? 

3. Why would it be unsatisfactory to construct a philosophy 
simply by taking as ultimate the most general laws and principles 
of physical science ? Can you mention any philosophers who have 
proceeded in this way? 

4. What is meant by the abstract or hypothetical character of 
the special sciences? Illustrate in the case of physics and psy- 
chology. 

5. Do the various sciences differ in their degree of abstract- 
ness ? If so, how would you classify them in order of concrete- 
ness? Compare mathematics and biology in this respect. 

6. Explain the function of philosophy as the interpretation of 
the results of the sciences. 

7. What is meant by the statement that philosophy must find 
a new category or principle of synthesis? Illustrate by showing 
what categories might conceivably be employed by philosophy. 



INDEX 



Abstract, two Meanings of the Word, 

Accent, the Fallacies of, 168. 

Accident, the Fallacy of, 178 f. 

A fortiori Arguments, 141. 

Agreement, the Method of, 239; Defi- 
ciencies in the Method of. 242-243. 

Amphiboly, the Fallacy of, 168. 

Analogy, Explanation by Means of, 
266; the Principle of, 268; State- 
ments of Law, 269; its Func- 
tion in suggesn'ng Hypothesis, 271; 
its Use by Darwin, 272; its Incom- 
pleteness as a Method of Explanation, 
274. 

Analysis, its Relation to Synthesis, 279. 

Analytic Procedure, 135 f. 

Anthropomorphism, 364. 

A priori Truths, 334. 

Argument, Irregular Forms of, 133 ff. 

Argumentum, ad rem, 184; ad homi- 
nem, 184 f • ; ad populum, 185 ; ad igno- 
rantiam, 186; ad verecundiam, 186; 
ad misericordiam^ 185; ad baculum, 
187. 

Aristotle, Logic of, 23; List of Logical 
Works, 23; his Theory of the Syllo- 
gism, 2^; as Founder of Modern 
Sciences, 23; Importance of In- 
duction and Deduction in his Logic, 
25; his^Classihcatioii of Fallacies, 164; 
his Statement of the Law of Con- 
tradiction, 350. 

Art, an, its Relation to a Science, 9 f. 



B 



Bacon, Logic of, 28; his Method, rC; 
on Induction by Simple Enumeration, 
193; on the Tendency to neglect 
Negative Instances, 310; his Doctrine 
of the Four Idols, 310-14 f. 

Bosanquet, his remarks on Analogy, 
276. 

Bradley, 13. 



Cant Words and Phrases, 302. 

Causal Connection, as Principle of 

Science, 235 f.; Judgments of, 362 ff. 
Cause, the Fallacy of the False, 189; 

the Development of the Principle of, 

362 ff. 
Causes, the Plurality of, 244. 
Chances, the Calculation of, 228. 
Circle, Argument in a, 181. 
Classification, Principles of, 79; Rules 

of, 81; of Fallacies, 165, 299; Aris- 
totle's, of Fallacies, 164. 
Composition, the Fallacy of, 174 f. 
Concepts, Relation to Percepts and 

Judgments, 44 fi"., 324 £f. 
Conclusion, the Irrelevant, 182. 
Concrete, two Senses of the Word, 51. 
Connotation, of Terms, 58 ff. 
Consequent, Fallacy of the, 187. 
Conservation of Energy, the Law of, 

and its Influence on the Conception 

of Cause, 366. 
Contradiction, the Law of, 38, 350, 
Conversion, the, of Propositions, 105; 

Simple, loi; by Limitation, 106; 

Errors in, 167. 



D 



Darwin, his Power of arresting Excep- 
tions, 263; his Use of Analogy, 
272 ; his Employment of Hypotheses, 
2 Si.' 

Deduction, its Relation to Induction, 

Definition, the Necessity of, 64; Verbal 
and Real, 66; W^ays of Regarding, 
67; Socrates' Search for, 68; Rules 
of, 70; Genetic, 74 ff. 

Denotation, of Terms, 58 ff.: Descartes, 

so- 
Dialectic, Socrates' Use of, 68. 
Dichotomy, 77. 
Difference, Method of, 244 f . 
Differentia, 70. 



5^7 



5i8 



Index 



Dilemma, the Simple Constructive, 157; 
the Complex Constructive, 158; 
the Simple Destructive, 157; the 
Complex Destructive, 159; the Fal- 
lacies of, 161 ff., 179, 

Division, Rules for, 81 ; the Fallac}' of, 
176. 

E 

Eduction, 99. 

Elimination, the Part of, in Induction, 
199, 289. 

Enthymemes, 40, 133. 

Enumeration, as the Starting-point of 
Induction, 194, 217; Judgments of, 

359- 

Episyllogisms and Prosyllogisms, 134. 

Equivocation, the Fallacies of, 172. 

Ethics, its Standpoint compared with, 
that of Psychology, 372. 

Euler, 92. 

Evolution, the Law of, 315; the Appli- 
cation of the Law of, to Thought, 

317 ff- 
Excluded Middle, the Law of, 77, 352. 
Experiment and Observation, 197; 

Advantages of employing, 211. 
Explanation and Observation, 207 f.; 

the Problem of, 212. 
Extension and Intension of Terms, 55. 



Fallacies, Classification of, 165, 299; 
Syllogistic, 165; Inductive, 298; the 
Source of, 298; of Interpretation, 
166; occasioned by Language, 299; 
of Reasoning, 170, 309; of Observa- 
tion, 303; Individual, 312. 

Figures of the Syllogism, 120; the 
Special Canons of the four, 123; De- 
termination of the Valid Moods in, 
127; the Perfect, 130; the Imperfect, 
130; Reduction of, 130; the Organic 
Relation of, 132 note. 



Galen, 130. 

Generalization, Danger of hasty, 310 f. 

Genus, its Definition, 70. 

Guericke, 287. 

H 

Hegel, his Influence on the Develop- 
ment of Logic, 32. 



Herschel, J., 31. 

H3-pothesis, as guiding Induction, 201; 
Reasoning from an, 278; the Employ- 
ment of, to explain Common Events, 
279; Darwin's Use of, 281; the 
Necessity for an, 282; Formation of, 
282 f.; the Function of Analogy in 
suggesting, 200, 284; the Proof of, 285 
ff.; Requirements of a Good, 293 ff. 



Identity, the Law of, 38, 343; Jev- 
ons's Interpretation of the Law of, 

344. 

Ignoratio Elenchi, 182. 

Imagination, its Part in the Formation 
of Theories, 282. 

Individuality, Judgments of, 370. 

Induction and Deduction, 384; the 
Baconian Method of, 28; Mill's 
Emphasis on, 31; the Problem of, 
190 f.; Perfect and Imperfect, 193 f. 

Inference, Mediate and Immediate, 97; 
the Nature of, 378; as distinguished 
from Judgment, 373; the Paradox 
of, 379; as a Development of Judg- 
ment, 378. (See also Reasonings) 

Instances, the Value of Numerous, i96f. 

Intension and Extension of Terms, 58 ff. 

Interpretation, of Propositions, 97 ff.; 
Errors of, 166; Judgment a Process 
of, 322. 

J 

James, 9. 

Jevons, his Account of Perfect Induc- 
tion, 193; his Calculation of Chances, 
228; his Interpretation of the Law 
of Identity, 344J his Principle of the 
Substitution of Similars, 345. 

Judgment, Relation to Perception and 
Conception, 44 ff., 324 ff.; the Start- 
ing-point of Knowledge, 7,22; as a 
Process of Interpretation, 323; and 
Concept, 324; the Universahty of , 329; 
the Necessity of, 331; a priori, 334; 
as involving both Analysis and Syn- 
thesis, 334 ff.; as constructing a Sys- 
tem of Knowledge, 339; its Relation 
to Inference, 373. 

Judgments, of Quality, 355; of Quan- 
tity, 358; of Enumeration, 359; of 
Measure, 360; of Causal Connec- 
tion, 362 ; of Individuality, 370. 



Index 



519 



Language, Relation to Thought, 3 f., 
46, 326; Dangers from the Careless 
Use of, 64, 298; Fallacies of, 299; 
Figurative, 302. 

Law, of Identity, t^^, 343; of Contra- 
diction, ^Z, 350; of Excluded Mid- 
dle, 77, 352; of Conservation of 
Energy, 367. 

Laws of Thought, ■^'^, 77, 343; on the 
Careless Use of Words, 64, 300. 

Logic, Definition of, i; Derivation of 
the Word, 3; Relation to Psychol- 
ogy, 5; Relation to Rhetoric, 3 f.; 
Comparison with Physiology, 7; as 
Normative Science, 6, 14; as a 
Science and an Art, 9; Utility of, 11 ; 
Necessity of, 13; the Materials of, 
14; of the Sophists, 20; of Socrates, 
20; of Aristotle, 23, 36; cf the School- 
men, 27; of Bacon, 28; of Mill, 31, 
34; Development 01 Modern , 32; 
the Equatfonai, 344. 

Lyell, his Overthrow of the 'Catas- 
trophic' Theory m Geology, 296. 



M 



Malthus, his Theories of Population, 

183, 273. 
Measure, Judgments of, 360. 
Metaphors, Dangers from the Use of, 

Method, the Progressive or Synthetic, 
135; the Regressive or Analytic, 135; 
the, of Agreement, 239; the, of Dif- 
ference, 244; the Joint, of Agreement 
and Difference, 249; the, of Con- 
comitant Variations, 255; the, of 
Residues, 260. 

Middle Term, the Function of the, 113; 
Ambiguous, 171. 

Mill, his Importance in the History of 
Logic, 31; his Experimental Meth- 
ods, 237. 

Mnemonic Lines, for Syllogism, 129. 

Moods, of Syllogism., 121. 

Morphology, compared with Psychol- 
ogy, 7- 

N 

Negative Instances, Tendency to neg- 
lect, 304. 



Neptune, the Discovery of, 264. 
Newton, his Care in testing Theories, 

28S. 
Non sequitur, 187. 
Normative Science, Logic as, 6, 14. 



O 



Observation, and Explanation, 207 fT. ; 
and Experiment, 211; Errors of, 

Obversion, the, of Propositions, 103; 

Errors in, 167. 
Opposition, the, of Propositions, 99. 



Perception, Relation to Conception and 
Judgment, 44 ff.; as involving Judg- 
ment, 45, 325; Difficulty in distin- 
guishing between Inference and, 308. 

Petitio Principii, 180. 

Philosophy and Science, 390; as inter- 
pretation of the sciences, 405. 

Physiology compared with Logic, 7. 

Plato, in the History of Logic, 27,; and 
the Doctrine of Reminiscence, 380. 

Post hoc propter hoc, 180, 310. 

Predicables, the, 69. 

Prejudices, Individual, 312; of an Age, 

Premises, Definition of, 40. 

Presumption, Fallacies of, 180. 

Propositions, Categorical, 85; Condi- 
tional, 85; the Nature of, 84; Qual- 
ity and Quantity of, 86; Difficul- 
ties in classifying, 89; Relation of 
Subject and Predicate in, 90; the 
Opposition of, 99; Contrary and 
Contradictory, 100; the Obversion 
of, 103; the Conveision of, 105; the 
Contraposition of, 107; the Inver- 
sion of, 109. 

Pro syllogisms, 134. 

Psychology, its Relation to Logic, 5; 
Comparison with Morphology, 7; 
Comparison with Ethics, 372. 



Quality, of Propositions, S6; Judg- 
ments of, 355. 

Quantity, of Propositions, 86; Judg- 
ments of, 358. 



520 



Index 



Quaiernio Terminorum, 1 70. 

Question, the Fallacy of the Complex, 

181. 
Question-Begging Epithet, 301. 



R 



Reasoning, the Nature of Syllogistic, 
112; Mediate, 97, 113; Immediate, 
97; Mistakes in, 309; Inductive and 
Deductive, 384; from Particulars to 
Particulars, 384; from Particulars to 
a Universal, 388. (See also Infer- 
ence.) 

Reduction of the Imperfect Figures, 
130. 

Residues, the Method of, 260. 



Scepticism, of the Sophists, 20 £f., 330. 
Schonbein, his Discovery of Ozone, 

263. 
Science, as related to Art, 9; as related 

to Philosophy, 390; as Philosophy, 

395; the Assumptions of, 399. 
Sigwart, on the Difference between 

Ancient and Modern Science, 219; 

on the Application of Statistics, 220. 
Similars, the Principle of the Substitu- 
^ tion of, 345- 
Socrates, his Place in the History of 

Logic, 20 ; his Search for Definitions, 

68; his Employment of Dialectic, 68. 
Sophists, the Logic of, 20; Socrates' 

Refutation of, 22; Plato's Criticism 

of their Theory of Knowledge, 22,', 

their Scepticism, 330. 
Sorites, Aristotelian, 137; Goclenian, 

Species, Definition, 70. 

Statistics, 219. 

Subject, Relation of Predicate- and, 90. 



Syllogism, the Aristotelian, 23, 36; the 
Nature of the, 36; the Principle of 
the, 37; the Parts of the, 39; the 
Rules of the, 115; the Figures of the, 
120; the Hypothetical, 143; Rules 
for the Hypothetical, 145; Relation 
of Categorical and Hypothetical, 148; 
the Disjunctive, 154; Fallacies of the 
Disjunctive, 156. 

Synthesis, its Relation to Analysis, 334. 

Synthetic Procedure, 135 f. 

System, Difference between a, and an 
Aggregate, 339. 



Terms, Definition of Logical, 49; 
Singular or Individual, 49; General 
and Collective, 49; Abstract and 
Concrete, 51 ff.; Positive and Nega- 
tive, 55; Contradictory and Con- 
trary, 56 f.; Privative, 56; Absolute 
and Relative, 57; Extension and 
Intension of, 58 ff. 

Thales, 365. 

Thought, its Relation to Language, 3f., 
46, 326; the Laws of, 2>^, 77, 343; 
as a process of Transformation and 
Conservation, 47 f; the Nature of, 316. 

TorriceUi, 287. 

U 

Unification of Knowledge, 390. 
Uniformity of Nature, 203, 236. 



Variations, of Statistics, 225; 
Method of Concomitant, 255. 

W 

Whewell, 16, 206. 

Words, the Abuse of, 65, 288. 



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